A007609 Values taken by the sigma function A000203, listed with multiplicity and in ascending order.

1, 3, 4, 6, 7, 8, 12, 12, 13, 14, 15, 18, 18, 20, 24, 24, 24, 28, 30, 31, 31, 32, 32, 36, 38, 39, 40, 42, 42, 42, 44, 48, 48, 48, 54, 54, 56, 56, 57, 60, 60, 60, 62, 63, 68, 72, 72, 72, 72, 72, 74, 78, 80, 80, 84, 84, 84, 90, 90, 90, 91, 93, 96, 96, 96, 96, 98, 98

Offset: 1

Author

Walter Nissen

Keywords

• nonn
• easy
• nice

Comments

A175192(a(n)) = 1, A054973(a(n)) >= 1. - Jaroslav Krizek, Mar 01 2010

a(n) is the median of the values of A000203(m) from m=1 to m=2n-1. (This needs confirmation as it relies on the assumption that A000203(n) is always bigger than the median of the values A000203(x) from x=1 to x=n.) - Chayim Lowen, May 27 2015

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A002191 (duplicates removed), A007368, A085790.

Programs

Maple

sort(select(`<=`,map(numtheory:-sigma,[$1..1000]),1001)); # Robert Israel, Jun 04 2015

Mathematica

terms = 68; ClearAll[t]; t[k_] := t[k] = Sort[ Table[ DivisorSigma[1, n], {n, 1, k*terms}]][[1 ;; terms]]; t[k = 2]; While[t[k] != t[k-1], k++]; t[k] (* Jean-François Alcover, Nov 21 2012 *)
With[{nn=80},Take[Sort[DivisorSigma[1,Range[nn*100]]],nn]] (* Harvey P. Dale, Mar 09 2016 *)

PARI

list(lim)=select(k->k<=lim,Set(apply(sigma,[1..lim\1]))) \\ Charles R Greathouse IV, Mar 09 2014

Formula

a(n) = sigma(A085790(n)). - Jinyuan Wang, Apr 15 2020