A347222 Numbers k for which sigma(k)/k = 12/5.

30, 140, 2480, 6200, 40640, 167751680, 42949345280, 687193456640, 11529215040699760640, 13292279957849158723273463079769210880, 957809713041180536473966890421518190654986607740846080, 65820182292848241686198767302293614551117361591934715588918640640

Offset: 1

Author

Timothy L. Tiffin, Aug 23 2021

Keywords

• nonn

Comments

This sequence will contain terms of the form 5*P, where P is a perfect number (A000396) not divisible by 5. Proof: sigma(5*P)/(5*P) = sigma(5)*sigma(P)/(5*P) = 6*(2*P)/(5*P) = 12/5. QED

Terms ending in "30", "40", or "80" have this form. Example: a(n) = 5*A000396(n) for n = 1, 2, 3 and a(n) = 5*A000396(n-1) for n = 5..12.

Examples

			6200 is a term, since sigma(6200)/6200 = 14880/6200 = 12/5.
		

Links

• G. P. Michon, Multiperfect Numbers and Hemiperfect Numbers
• Walter Nissen, Abundancy: Some Resources (preliminary version 4)
• Walter Nissen, Primitive Friendly Pairs with friends < 2^34 with denom < 20000

Crossrefs

Cf. A000203, A000396.

Subsequence of A005101 and A218407.

Programs

Mathematica

Select[Range[5*10^8], DivisorSigma[1, #]/# == 12/5 &]
Do[If[DivisorSigma[1, k]/k == 12/5, Print[k]], {k, 5*10^8}]

Extensions

a(9)-a(10) from Michel Marcus, Aug 24 2021

a(11)-a(12) from David A. Corneth, Aug 24 2021