A211779 a(n) = Sum_{d_<n | n} sigma(d_<n), where d_<n = divisors of n that are less than n, sigma(x) = A000203(x).

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, 43, 1, 68, 1, 57, 17, 22, 15, 107, 1, 24, 19, 92, 1, 84, 1, 59, 48, 28, 1, 161, 9, 59, 23, 67, 1, 112, 19, 114, 25, 34, 1, 217, 1, 36, 58, 120, 21, 116, 1, 83, 29

Offset

1,4

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..27144 (first 1000 terms from Jaroslav Krizek)

Index entries for sequences related to sums of divisors.

Formula

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

G.f.: sum(n>=1, A000203(n)*x^(2*n)/(1-x^n) ). - Mircea Merca, Feb 26 2014

a(n) = Sum_{d|n} A001065(d). - Antti Karttunen, Nov 13 2017

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

Mathematica

Table[Sum[DivisorSigma[1, d], {d, Most[Divisors[n]]}], {n, 100}] (* T. D. Noe, Apr 26 2012 *)

Prog

(PARI) a(n)=sumdiv(n, d, sigma(d))-sigma(n) \\ Charles R Greathouse IV, Feb 19 2013

Crossrefs

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

Sequence in context: A240776 A019768 A319296 * A318445 A158496 A265722

Adjacent sequences: A211776 A211777 A211778 * A211780 A211781 A211782

Keyword

nonn

Author

Jaroslav Krizek, Apr 20 2012

Status

approved