A360721 - OEIS

A360721

a(n) is the number of infinitary divisors of n that are powerful (A001694).

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

Index entries for sequences related to divisors of numbers.

FORMULA

Multiplicative with a(p^e) = 2^A000120(e) - (e mod 2).

a(n) <= A037445(n) with equality if and only if n is a square.

a(n) <= A005361(n) with equality if and only if n is not in A360723.

Sum_{k=1..n} a(k) a(k) ~ c * n, where c = Product_{p prime} ((1-1/p) * Sum_{k>=1} ((2^A000120(k)- k mod 2)/p^k)) = 1.72717... .