A008332 Sum of divisors of p-1, p prime.

1, 3, 7, 12, 18, 28, 31, 39, 36, 56, 72, 91, 90, 96, 72, 98, 90, 168, 144, 144, 195, 168, 126, 180, 252, 217, 216, 162, 280, 248, 312, 252, 270, 288, 266, 372, 392, 363, 252, 308, 270, 546, 360, 508, 399, 468, 576, 456, 342, 560, 450, 432, 744, 468, 511, 396, 476, 720, 672

Offset

1,2

Comments

For all n (except for n = 2) gcd(A008332(n), prime(n)) = 1. - Lechoslaw Ratajczak, Aug 22 2018

References

Yu. V. Linnik. The dispersion method in binary additive problems, Izdat. Leningrad Univ., Leningrad, 1961.

József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 87.

Links

Michel Marcus, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Formula

a(n) = A000203(A006093(n)). - Michel Marcus, Aug 19 2018

Sum_{k=1..n} a(k) ~ (zeta(2)*zeta(3)/zeta(6)) * n + O(n/log(n)^0.999) (Linnik, 1961). - Amiram Eldar, Mar 04 2021

Maple

for i from 1 to 500 do if isprime(i) then print(sigma(i-1)); fi; od;

Mathematica

Table[DivisorSigma[1, Prime[n] - 1], {n, 80}] (* Vincenzo Librandi, Aug 20 2018 *)

Prog

(PARI) a(n) = sigma(prime(n)-1); \\ Michel Marcus, Aug 19 2018
(Magma) [DivisorSigma(1, NthPrime(n)-1): n in [1..60]]; // Vincenzo Librandi, Aug 20 2018

Crossrefs

Cf. A000203, A006093, A008332, A082695.

Sequence in context: A024388 A184534 A109638 * A065390 A171835 A324125

Adjacent sequences: A008329 A008330 A008331 * A008333 A008334 A008335

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

Offset corrected by Michel Marcus, Aug 20 2018

Status

approved