A356242 - OEIS

A356242

a(n) is the number of Fermat numbers dividing n, counted with multiplicity.

0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 1, 0, 0, 1, 2, 0, 3, 0, 0, 2, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 3, 0, 0, 1, 0, 2, 2, 0, 0, 3, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 3, 0, 0, 1, 0, 1, 4, 0, 0, 1, 2, 0, 1

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OFFSET

1,9

COMMENTS

The multiplicity of a divisor d (not necessarily a prime) of n is defined in A169594 (see also the first formula).

A000244(n) is the least number k such that a(k) = n.

The asymptotic density of occurrences of 0 is 1/2.

The asymptotic density of occurrences of 1 is (1/2) * Sum_{k>=0} 1/(2^(2^k)+1) = (1/2) * A051158 = 0.2980315860... .

LINKS

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

Eric Weisstein's World of Mathematics, Fermat Number.

Wikipedia, Fermat number.