In number theory, the gcd-sum function, also called Pillai's arithmetical function, is defined for every n {\displaystyle n} by P ( n ) = ∑ k = 1 n gcd...

Subbayya Sivasankaranarayana Pillai (5 April 1901 – 31 August 1950) was an Indian mathematician specialising in number theory. His contribution to Waring's...

_{k|a{\text{ and }}k|b}\varphi (k).} GCD Summatory function (Pillai's arithmetical function): ∑ k = 1 n gcd ( k , n ) = ∑ d | n d φ ( n d ) = n ∑ d | n...

is Liouville's function. Id ∗ ϕ = P {\displaystyle {\text{Id}}*\phi =P} , where P {\displaystyle P} is Pillai's arithmetical function, also known as the...

Sivasankaranarayana Pillai - Indian mathematician and inventor of Pillai's conjecture, Pillai's arithmetical function, Pillai prime, Pillai sequence. M.S.S...

sequence would require "hundreds of millions of digits". Pillai, S. S. (1930), "An arithmetical function concerning primes", Annamalai University Journal: 159–167...

conjecture Euler's sum of powers conjecture abc Conjecture Catalan's conjecture Pillai's conjecture Hasse principle Diophantine set Matiyasevich's theorem Hundred...

277. Billingsley 1995, Section 19. Edwards, A.W.F (2002). Pascal's arithmetical triangle: the story of a mathematical idea (2nd ed.). JHU Press. ISBN 0-8018-6946-3...

perfect powers is 23 = 8 and 32 = 9, thus proving Catalan's conjecture. Pillai's conjecture states that for any given positive integer k there are only...

below.) Bhaskara's arithmetic text Līlāvatī covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions...

particular, the Riemann zeta function). The first such distribution found is π(N) ~ ⁠N/log(N)⁠, where π(N) is the prime-counting function (the number of primes...

68 (6): 557–560. doi:10.2307/2311150. JSTOR 2311150. S. S. Pillai, "An arithmetical function concerning primes", Annamalai University Journal (1930), pp...

contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid...

to be of roughly comparable difficulty. The Goldbach partition function is the function that associates to each even integer the number of ways it can...

{\displaystyle \sigma (n)>\sigma (m)} where σ denotes the sum-of-divisors function. The first few highly abundant numbers are 1, 2, 3, 4, 6, 8, 10, 12, 16...

Sreedharan Pillai–M. S. Bartlett trace, Λ Pillai = ∑ 1 , … , p ( λ p / ( 1 + λ p ) ) = tr ⁡ ( A ( I + A ) − 1 ) {\displaystyle \Lambda _{\text{Pillai}}=\sum...

certain arithmetical functions", Ramanujan defined the so-called delta-function, whose coefficients are called τ(n) (the Ramanujan tau function). He proved...

(1996). "The Development of Arithmetical Thinking: On the Role of Calculating Aids in Ancient Egyptian & Babylonian Arithmetic". Abstraction & Representation:...

India. He specialized in number theory, in particular the theory of arithmetic functions. Known to his friends as CSV, Venkataraman was born at Chelakkara...

fact examples had been found earlier of functions that were nowhere differentiable (see Weierstrass function). According to Weierstrass in his paper,...

in exactly one normalized solution to the Markov Diophantine equation. Pillai's conjecture: for any A , B , C {\displaystyle A,B,C} , the equation A x...

new values of the sine function from other values already tabulated. The formula gives an estimate for the value of a function f at a value a + xh of...

Rashed, Roshdi (1994). The development of Arabic mathematics: between arithmetic and algebra. Vol. 156. Dordrecht, Boston, London: Kluwer Academic Publishers...

_{j=1}^{i}p_{j}} , and pj = jth prime, p0# = p0 = 1. S. S. Pillai, "An arithmetical function concerning primes", Annamalai University Journal (1930), pp...

century) was an Indian mathematician, known for two extant treatises about arithmetic and practical mathematics, Pāṭīgaṇita and Pāṭīgaṇita-sāra, and a now-lost...

Arithmetic functions and dynamics...

also be considered. SPSS provides an F-ratio from four different methods: Pillai's trace, Wilks’ lambda, Hotelling's trace, and Roy's largest root. In general...

number is known as a "Martian prime". Cunningham chain Double exponential function Fermat number Perfect number Wieferich prime Chris Caldwell, Mersenne Primes:...

Arithmetic functions and dynamics...

medieval Arabs and Persians, they called it al-ḥisāb al-hindī ("Indian arithmetic"). These numerals were gradually adopted in Europe starting around the...