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A275321
Numbers n such that denominator(sigma(sigma(n))/n) = denominator(sigma(sigma(s))/s) where s = sigma(n).
0
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)?
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
Sequence in context: A063534 A361420 A162651 * A022320 A318387 A349908
KEYWORD
nonn
AUTHOR
Michel Marcus, Jul 23 2016
STATUS
approved