A237286 -id:A237286 - cp's OEIS frontend

A070310 Numbers n such that the sum of its aliquot parts and the number of its divisors are both perfect numbers.

28, 652, 10828

Offset: 1

Jason Earls, May 10 2002

Subsequence of A237286. - Roderick MacPhee, Jan 19 2017

p = {6, 28, 496, 8128, 33550336}; Do[a = Divisors[n]; If[ Position[p, Plus @@ Drop[a, -1]] != {} && Position[p, Length[a]] != {}, Print[n]], {n, 1, 10^7}]

{for(n=1,10^8,d=numdiv(n); if(d==sigma(d)-d,s=sigma(n)-n; if(s==sigma(s)-s,print1(n,","))))}

Edited by Robert G. Wilson v, May 14 2002

No further terms below 10^8. Is the sequence complete? - Klaus Brockhaus, May 17 2002

A382504 Numbers k such that one or both of sigma(k) + k and sigma(k) - k is a perfect number.

Original entry on oeis.org

6, 10, 25, 28, 496, 652, 8128, 10682, 10828, 33550336, 44655764, 8589869056, 8623554304

Offset: 1

Leo Hennig, Mar 29 2025

10 and 838476969534191044 are the only known numbers k for which sigma(k) + k is a perfect number.

			sigma(6) = 12 and 12 - 6 = 6.
sigma(10) = 18 and 18 + 10 = 28.
sigma(25) = 31 and 31 - 25 = 6.

Leo Hennig, One entry and just one entry, Seqfan thread.

Supersequence of A000396 and of A237286.

Cf. A000203.

isp(x) = if (x>0, sigma(x) == 2*x);
isok(x) = isp(sigma(x)-x) || isp(sigma(x)+x); \\ Michel Marcus, Mar 29 2025

cp's OEIS Frontend

A070310 Numbers n such that the sum of its aliquot parts and the number of its divisors are both perfect numbers.

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