A347261 -id:A347261

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A341623

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

+10
1

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

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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.

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

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