A330598 Numbers k such that the denominator of sigma(sigma(k))/k is equal to 2.

30, 2046, 245760, 301056, 450560, 1171456, 1351680, 3514368, 14515200, 16760832, 19611648, 77220864, 159373824, 357291648, 391444480, 477216768, 555714432, 754928640, 765414240, 1006602240, 1761500160, 2330913312, 4314834944, 8369053056, 20449394784, 37949317120

Offset: 1

Author

Michel Marcus, Dec 19 2019

Keywords

• nonn

Comments

Although the definition here is similar to the one in A019278, it appears that this sequence does not have the same nice features as A019278.

Otherwise said: sigma(sigma(k))/k is half-integer, or: sigma(sigma(k)) is an odd multiple of k/2. This also implies that all terms are even. - M. F. Hasler, Jan 06 2020

Examples

			sigma(sigma(30))/30 = sigma(72)/30 = 195/30 = 13/2 so 30 is a term.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..38 (terms < 10^13)
• Michel Marcus, Unexhaustive list of terms

Crossrefs

Cf. A019278 (denominator is 1), A051027 (sigma(sigma)).

Cf. A000203 (sigma), A159907 (hemiperfect numbers).

Programs

PARI

isok(n) = denominator(sigma(sigma(n))/n) == 2;

Extensions

a(22)-a(26) from Giovanni Resta, Dec 20 2019