A275321 - OEIS

%I #5 Jul 23 2016 09:59:40

%S 1,6,8,15,24,28,60,168,512,1023,1536,4092,10752,12600,14040,18564,

%T 24384,29127,47360,57120,89408,116508,306306,331520,343976,687952,

%U 932064,1556480,1571328,1980342,2207520,3655680,3932040,4404480,4761600,31683960,43570800,82378296

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

%C 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.

%C 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, ...

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

%e For n=1, sigma(1)=1, so 1 is obviously in the sequence.

%e 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.

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

%Y Cf. A051027, A019278.

%K nonn

%O 1,2

%A _Michel Marcus_, Jul 23 2016