A320024 The odd part of those numbers which divide the sum of their divisors (A007691).

1, 3, 7, 15, 31, 21, 127, 945, 4095, 1023, 544635, 46035, 8191, 355725, 279279, 1796165, 5388495, 180213, 131071, 110800305, 249987465, 42833475, 3112865, 8109585, 524287, 9338595, 49198149, 253255275, 22017975903, 13341660255, 30101431815, 709933138551

Offset: 1

Author

Peter Luschny, Oct 03 2018

Keywords

• nonn

Comments

The data was derived from the data in A007691.

The Mersenne primes A000668 are a subsequence; in fact a prime is in this sequence if and only if it is a Mersenne prime.

Note that John Voight's 'spoof odd perfect number' 22017975903 is included. - Peter Luschny, Oct 30 2020

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1600
• BYU Computational Number Theory Group, Odd, spoof perfect factorizations, arXiv:2006.10697 [math.NT], 2020.
• J. Voight, On the nonexistence of odd perfect numbers.

Crossrefs

Cf. A000265, A000668, A007691.

Programs

Maple

a_list := proc(len) local L, n; L := NULL; for n from 1 to len do
if numtheory:-sigma(n) mod n = 0 then L := L, n/2^padic[ordp](n, 2) fi od; L end:

Mathematica

A007691 = Select[Range[1000000], Divisible[DivisorSigma[1, #], #] &]; Table[A007691[[n]]/2^IntegerExponent[A007691[[n]], 2], {n, 1, Length[A007691]}] (* Vaclav Kotesovec, Oct 14 2018 *)

Formula

a(n) = A000265(A007691(n)).