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

%I A008332 #41 Jul 20 2025 03:24:19
%S A008332 1,3,7,12,18,28,31,39,36,56,72,91,90,96,72,98,90,168,144,144,195,168,
%T A008332 126,180,252,217,216,162,280,248,312,252,270,288,266,372,392,363,252,
%U A008332 308,270,546,360,508,399,468,576,456,342,560,450,432,744,468,511,396,476,720,672
%N A008332 Sum of divisors of p-1, p prime.
%C A008332 For all n (except for n = 2) gcd(A008332(n), prime(n)) = 1. - _Lechoslaw Ratajczak_, Aug 22 2018
%D A008332 József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 87.
%H A008332 Michel Marcus, <a href="/A008332/b008332.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Vincenzo Librandi)
%H A008332 William A. Webb, <a href="https://doi.org/10.1215/S0012-7094-71-03871-3">An asymptotic estimate for a class of divisor sums</a>, Duke Math. J., Vol. 38, No. 3 (1971), pp. 575-582.
%F A008332 a(n) = A000203(A006093(n)). - _Michel Marcus_, Aug 19 2018
%F A008332 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]
%p A008332 for i from 1 to 500 do if isprime(i) then print(sigma(i-1)); fi; od;
%t A008332 Table[DivisorSigma[1, Prime[n] - 1], {n, 80}] (* _Vincenzo Librandi_, Aug 20 2018 *)
%o A008332 (PARI) a(n) = sigma(prime(n)-1); \\ _Michel Marcus_, Aug 19 2018
%o A008332 (Magma) [DivisorSigma(1, NthPrime(n)-1): n in [1..60]]; // _Vincenzo Librandi_, Aug 20 2018
%Y A008332 Cf. A000203, A006093, A008332, A065484.
%K A008332 nonn,easy
%O A008332 1,2
%A A008332 _N. J. A. Sloane_
%E A008332 Offset corrected by _Michel Marcus_, Aug 20 2018