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

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

Offset: 1

Author

Antti Karttunen, Feb 19 2021

Keywords

• nonn
• more

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

Examples

			546 is a term, since sigma(3*546) = sigma(1638) = 4368 = 8*546. - _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.

Programs

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 *)

Extensions

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

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