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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

References

• 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)
• William A. Webb, An asymptotic estimate for a class of divisor sums, Duke Math. J., Vol. 38, No. 3 (1971), pp. 575-582.

Crossrefs

Cf. A000203, A006093, A008332, A065484.

Programs

Magma

[DivisorSigma(1, NthPrime(n)-1): n in [1..60]]; // Vincenzo Librandi, Aug 20 2018

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 *)

PARI

a(n) = sigma(prime(n)-1); \\ Michel Marcus, Aug 19 2018

Formula

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

Sum_{k; prime(k)<=x} a(k) ~ c * x^2/(2*log(x)), where c = A065484 (Webb, 1971). - Amiram Eldar, Mar 04 2021 [corrected Jul 20 2025]

Extensions

Offset corrected by Michel Marcus, Aug 20 2018