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A320024
The odd part of those numbers which divide the sum of their divisors (A007691).
3
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
BYU Computational Number Theory Group, Odd, spoof perfect factorizations, arXiv:2006.10697 [math.NT], 2020.
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Oct 03 2018
STATUS
approved