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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 (list; graph; refs; listen; history; text; internal format)
 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 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: A315926 A063534 A162651 * A022320 A318387 A349908 Adjacent sequences:  A275318 A275319 A275320 * A275322 A275323 A275324 KEYWORD nonn AUTHOR Michel Marcus, Jul 23 2016 STATUS approved

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Last modified August 9 21:08 EDT 2022. Contains 356026 sequences. (Running on oeis4.)