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

1,1

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

Links

Giovanni Resta, Table of n, a(n) for n = 1..38 (terms < 10^13)

Michel Marcus, Unexhaustive list of terms

Example

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

Prog

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

Crossrefs

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

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

Sequence in context: A280670 A092608 A241128 * A255958 A092617 A295446

Adjacent sequences: A330595 A330596 A330597 * A330599 A330600 A330601

Keyword

nonn

Author

Michel Marcus, Dec 19 2019

Extensions

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

Status

approved