This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A039653 #37 Mar 14 2023 12:54:21
%S A039653 0,0,2,3,6,5,11,7,14,12,17,11,27,13,23,23,30,17,38,19,41,31,35,23,59,
%T A039653 30,41,39,55,29,71,31,62,47,53,47,90,37,59,55,89,41,95,43,83,77,71,47,
%U A039653 123,56,92,71,97,53,119,71,119,79,89,59,167,61,95,103,126,83,143,67,125,95
%N A039653 a(0) = 0; for n > 0, a(n) = sigma(n)-1.
%C A039653 Call an integer k between 1 and n a "semi-divisor" of n if n leaves a remainder of 1 when divided by k, i.e., n == 1 (mod k). a(n) gives the sum of the semi-divisors of n+1. - _Joseph L. Pe_, Sep 11 2002
%C A039653 a(n) is also the sum of the strong divisors of n, for n >= 1. - _Omar E. Pol_, May 01 2015
%H A039653 Antti Karttunen, <a href="/A039653/b039653.txt">Table of n, a(n) for n = 0..10000</a>
%H A039653 OEIS Wiki, <a href="https://oeis.org/wiki/Cyclotomic Polynomials at x=n, n! and sigma(n)">Cyclotomic Polynomials at x=n, n! and sigma(n)</a>
%F A039653 a(p) = p for p prime.
%F A039653 G.f.: -2*x^2/(Q(0) - 2*x^2 + 2*x), where Q(k) = (2*x^(k+2) - x - 1)*k - 1 - 2*x + 3*x^(k+2) - x*(k+3)*(k+1)*(1-x^(k+2))^2/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, May 16 2013
%F A039653 Let A(x) be the g.f. of A039653 and B(x) the g.f. of A155085. Then B(x) = 1/(1-x) + 1/(1-x)^2 + A(x)/x. - _Sergei N. Gladkovskii_, May 16 2013
%p A039653 with(numtheory): A039653:=n->sigma(n)-1: (0, seq(A039653(n), n=1..100)); # _Wesley Ivan Hurt_, Jul 09 2015
%t A039653 Join[{0}, Table[DivisorSigma[1, n] - 1, {n, 90}]] (* _Vincenzo Librandi_, May 02 2015 *)
%o A039653 (Magma) [0] cat [DivisorSigma(1, n)-1: n in [1..100]]; // _Vincenzo Librandi_, May 02 2015
%o A039653 (PARI) A039653(n) = if(!n,n,sigma(n)-1); \\ _Antti Karttunen_, May 26 2017
%o A039653 (Python)
%o A039653 from sympy import divisor_sigma
%o A039653 def A039653(n): return divisor_sigma(n)-1 if n else 0 # _Chai Wah Wu_, Mar 14 2023
%Y A039653 Cf. A000203, A039649, A039650, A039651, A039652, A039653, A039654, A039655, A039656, A032741.
%K A039653 nonn
%O A039653 0,3
%A A039653 _David W. Wilson_