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

1,4

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A111397 A131743 A357860 * A363879 A366767 A113686

Adjacent sequences: A147645 A147646 A147647 * A147649 A147650 A147651

Keyword

easy,nonn

Author

Omar E. Pol, Nov 09 2008

Status

approved