A347169 Numbers k for which sigma(k)/k = 16/7.

42, 3472, 56896, 544635, 234852352, 60129083392, 962070839296, 16140901056979664896, 18609191940988822212582848311676895232

Offset: 1

Author

Timothy L. Tiffin, Aug 20 2021

Keywords

• nonn
• more

Comments

This sequence will contain terms of the form 7*P, where P is a perfect number (A000396) not divisible by 7. Proof: sigma(7*P)/(7*P) = sigma(7)*sigma(P)/(7*P) = 8*(2*P)/(7*P) = 16/7. QED

Terms ending in "2" or "96" have this form. Example: a(n) = 7*A000396(n) for n = 1, 5, 6, 7, 8, 9 and a(n) = 7*A000396(n+1) for n = 2, 3.

Examples

			544635 is a term, since sigma(544635)/544635 = 1244880/544635 = 16/7.
		

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 A218409.

Programs

Mathematica

Select[Range[5*10^8], DivisorSigma[1, #]/# == 16/7 &]
Do[If[DivisorSigma[1, k]/k == 16/7, Print[k]], {k, 5*10^8}]

Extensions

a(8)-a(9) from Michel Marcus, Aug 21 2021