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Number of distinct even superperfect numbers dividing n.
2

%I #11 Jan 01 2024 07:59:10

%S 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 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 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 Number of distinct even superperfect numbers dividing n.

%C Also, numbers of distinct superperfect numbers dividing n, if there are no odd superperfect numbers.

%H Antti Karttunen, <a href="/A147648/b147648.txt">Table of n, a(n) for n = 1..65537</a>

%F 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 Array[DivisorSum[#, 1 &, And[EvenQ@ #, Nest[DivisorSigma[1, #] &, #, 2] == 2 #] &] &, 105] (* _Michael De Vlieger_, Nov 06 2018 *)

%o (PARI) A147648(n) = sumdiv(n,d,(!(d%2)&&(sigma(sigma(d))==(2*d)))); \\ _Antti Karttunen_, Nov 06 2018

%Y Cf. A001221, A019279, A061652, A080225, A147645.

%K easy,nonn

%O 1,4

%A _Omar E. Pol_, Nov 09 2008