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

1,2

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.

Formula

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

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 *)

Crossrefs

Cf. A000265, A000668, A007691.

Sequence in context: A069112 A064084 A090633 * A098583 A275531 A275532

Adjacent sequences: A320021 A320022 A320023 * A320025 A320026 A320027

Keyword

nonn

Author

Peter Luschny, Oct 03 2018

Status

approved