A211779 - OEIS

%I #30 Mar 17 2024 03:18:08

%S 0,1,1,4,1,8,1,11,5,10,1,27,1,12,11,26,1,33,1,35,13,16,1,70,7,18,18,

%T 43,1,68,1,57,17,22,15,107,1,24,19,92,1,84,1,59,48,28,1,161,9,59,23,

%U 67,1,112,19,114,25,34,1,217,1,36,58,120,21,116,1,83,29

%N a(n) = Sum_{d_<n | n} sigma(d_<n), where d_<n = divisors of n that are less than n, sigma(x) = A000203(x).

%C The numbers n < 1000 such that n divides a(n) are 4, 10, 42, and 90. (See A224488).

%H Antti Karttunen, <a href="/A211779/b211779.txt">Table of n, a(n) for n = 1..27144</a> (first 1000 terms from Jaroslav Krizek)

%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.

%F a(n) = A007429(n) - A000203(n) = A211780(n) - A000203(n) + n.

%F G.f.: sum(n>=1, A000203(n)*x^(2*n)/(1-x^n) ). - _Mircea Merca_, Feb 26 2014

%F a(n) = Sum_{d|n} A001065(d). - _Antti Karttunen_, Nov 13 2017

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^4/72 - Pi^2/12 = 0.530437... . - _Amiram Eldar_, Mar 17 2024

%t Table[Sum[DivisorSigma[1, d], {d, Most[Divisors[n]]}], {n, 100}] (* _T. D. Noe_, Apr 26 2012 *)

%o (PARI) a(n)=sumdiv(n,d,sigma(d))-sigma(n) \\ _Charles R Greathouse IV_, Feb 19 2013

%Y Cf. A000203, A007429, A001065, A211780, A224488.

%K nonn

%O 1,4

%A _Jaroslav Krizek_, Apr 20 2012