cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A147648 Number of distinct even superperfect numbers dividing n.

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%I A147648 #11 Jan 01 2024 07:59:10
%S A147648 0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,3,0,1,
%T A147648 0,2,0,1,0,2,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,4,0,1,0,2,
%U A147648 0,1,0,2,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,3,0,1,0,2
%N A147648 Number of distinct even superperfect numbers dividing n.
%C A147648 Also, numbers of distinct superperfect numbers dividing n, if there are no odd superperfect numbers.
%H A147648 Antti Karttunen, <a href="/A147648/b147648.txt">Table of n, a(n) for n = 1..65537</a>
%F A147648 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{n>=1} 1/A061652(n) = 0.828388215042... . - _Amiram Eldar_, Jan 01 2024
%t A147648 Array[DivisorSum[#, 1 &, And[EvenQ@ #, Nest[DivisorSigma[1, #] &, #, 2] == 2 #] &] &, 105] (* _Michael De Vlieger_, Nov 06 2018 *)
%o A147648 (PARI) A147648(n) = sumdiv(n,d,(!(d%2)&&(sigma(sigma(d))==(2*d)))); \\ _Antti Karttunen_, Nov 06 2018
%Y A147648 Cf. A001221, A019279, A061652, A080225, A147645.
%K A147648 easy,nonn
%O A147648 1,4
%A A147648 _Omar E. Pol_, Nov 09 2008