A341623 Numbers k such that sigma(3*k) = 8*k.

28, 90, 496, 546, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, 2658455991569831744654692615953842176

Offset

1,1

Comments

Every perfect number P greater than 6 (so, P is not divisible by 3) will be found in this sequence. Proof: sigma(3*P) = sigma(3)*sigma(P) = 4*(2*P) = 8*P. - Timothy L. Tiffin, Aug 26 2021

Solutions are integers y/3 where sigma(y)/y = 8/3. - Michel Marcus, Aug 27 2021

Links

Table of n, a(n) for n=1..10.

Example

546 is a term, since sigma(3*546) = sigma(1638) = 4368 = 8*546. - Timothy L. Tiffin, Aug 26 2021

Mathematica

Select[Range[5*10^9], DivisorSigma[1, 3*#] == 8*# &] (* Timothy L. Tiffin, Aug 26 2021 *)
Do[If[DivisorSigma[1, 3*k] == 8*k, Print[k]], {k, 5*10^9}] (* Timothy L. Tiffin, Aug 26 2021 *)

Crossrefs

Cf. A000396 (subsequence, apart from its terms that are divisible by 3).

Subsequence of A005101 and A227303.

Cf. also A000203, A144613, A326051, A336702, A347261.

Sequence in context: A164689 A096384 A065655 * A272399 A113958 A219815

Adjacent sequences: A341620 A341621 A341622 * A341624 A341625 A341626

Keyword

nonn,more

Author

Antti Karttunen, Feb 19 2021

Extensions

a(7)-a(8) from Martin Ehrenstein, Mar 06 2021

a(9)-a(10) from Michel Marcus, Aug 27 2021

Status

approved