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

1,2

Comments

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

Links

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

Example

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

Mathematica

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

Prog

(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}

Crossrefs

Odd terms of A327165.

Cf. A064987.

Sequence in context: A217798 A252853 A273125 * A326064 A233376 A233051

Adjacent sequences: A327596 A327597 A327598 * A327600 A327601 A327602

Keyword

nonn

Author

David A. Corneth, Sep 18 2019

Status

approved