A275321 Numbers n such that denominator(sigma(sigma(n))/n) = denominator(sigma(sigma(s))/s) where s = sigma(n).

1, 6, 8, 15, 24, 28, 60, 168, 512, 1023, 1536, 4092, 10752, 12600, 14040, 18564, 24384, 29127, 47360, 57120, 89408, 116508, 306306, 331520, 343976, 687952, 932064, 1556480, 1571328, 1980342, 2207520, 3655680, 3932040, 4404480, 4761600, 31683960, 43570800, 82378296

Offset

1,2

Comments

This sequence is motivated by the existence in A019278 of terms n such that s=sigma(n) is also a term of A019278. Those terms are a subsequence of this sequence.

The corresponding denominators are 1, 3, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 5, 15, 28, 127, 1, 1, 1, 127, 1, 39, 1, 1, 31, 1, 1, 682, 1, 9, 16, 1, 1, 310, 99, 1729, ...

Are there other terms, like 1 and 6 (see example)?

Links

Table of n, a(n) for n=1..38.

Example

For n=1, sigma(1)=1, so 1 is obviously in the sequence.
For n=6, sigma(6)=12; sigma(sigma(6))/6 and sigma(sigma(12))/12 are both equal to 14/3, so they have same denominator 3; so 6 is in the sequence.

Prog

(PARI) isok(n) = {my(s = sigma(n), ss=sigma(s)); denominator(ss/n) == denominator(sigma(ss)/s); };

Crossrefs

Cf. A051027, A019278.

Sequence in context: A063534 A361420 A162651 * A022320 A318387 A349908

Adjacent sequences: A275318 A275319 A275320 * A275322 A275323 A275324

Keyword

nonn

Author

Michel Marcus, Jul 23 2016

Status

approved