A327599 Odd numbers k that have a divisor d such that sigma(d)*d is equal to k.

1, 117, 775, 2793, 9801, 16093, 30927, 88723, 90675, 137541, 292537, 326781, 488125, 732511, 796797, 954273, 1882881, 1926183, 2164575, 2896363, 3500157, 3618459, 4985713, 6725201, 7595775, 8042167, 10380591, 12326221, 12472075, 14076543, 16092297, 20456373, 23968425, 25774633

Offset: 1

Author

David A. Corneth, Sep 18 2019

Keywords

• nonn

Comments

We need d and sigma(d) odd which happens precisely when d is an odd square.

Examples

			As 9 * sigma(9) = 9 * (1 + 3 + 9) = 9 * 13 = 117 is odd, 117 is in the sequence.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Odd terms of A327165.

Cf. A064987.

Programs

Mathematica

Select[2Range[0, 9999] + 1, MemberQ[(DivisorSigma[1, #] * # &)/@Divisors[#], #] &] (* Alonso del Arte, Sep 18 2019 *)

PARI

upto(n) = {my(res = List()); forstep(i = 1, sqrtnint(n, 4), 2, c = i^2*sigma(i^2); if(c <= n, listput(res, c))); listsort(res, 1); res}