A008332 - OEIS

%I #35 Sep 08 2022 08:44:35

%S 1,3,7,12,18,28,31,39,36,56,72,91,90,96,72,98,90,168,144,144,195,168,

%T 126,180,252,217,216,162,280,248,312,252,270,288,266,372,392,363,252,

%U 308,270,546,360,508,399,468,576,456,342,560,450,432,744,468,511,396,476,720,672

%N Sum of divisors of p-1, p prime.

%C For all n (except for n = 2) gcd(A008332(n), prime(n)) = 1. - _Lechoslaw Ratajczak_, Aug 22 2018

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

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

%H Michel Marcus, <a href="/A008332/b008332.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Vincenzo Librandi)

%F a(n) = A000203(A006093(n)). - _Michel Marcus_, Aug 19 2018

%F 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

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

%t Table[DivisorSigma[1, Prime[n] - 1], {n, 80}] (* _Vincenzo Librandi_, Aug 20 2018 *)

%o (PARI) a(n) = sigma(prime(n)-1); \\ _Michel Marcus_, Aug 19 2018

%o (Magma) [DivisorSigma(1, NthPrime(n)-1): n in [1..60]]; // _Vincenzo Librandi_, Aug 20 2018

%Y Cf. A000203, A006093, A008332, A082695.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_.

%E Offset corrected by _Michel Marcus_, Aug 20 2018