A147648 Number of distinct even superperfect numbers dividing n.

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, 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, 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

Offset: 1

Author

Omar E. Pol, Nov 09 2008

Keywords

• easy
• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

Programs

Mathematica

Array[DivisorSum[#, 1 &, And[EvenQ@ #, Nest[DivisorSigma[1, #] &, #, 2] == 2 #] &] &, 105] (* Michael De Vlieger, Nov 06 2018 *)

PARI

A147648(n) = sumdiv(n,d,(!(d%2)&&(sigma(sigma(d))==(2*d)))); \\ Antti Karttunen, Nov 06 2018

Formula

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