A366075 The number of primes dividing the smallest coreful infinitary divisor of n, counted with multiplicity.

0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 2, 2, 2, 1, 3, 1, 3, 1, 1, 2, 2, 2, 4, 1, 2, 2, 2, 1, 3, 1, 3, 3, 2, 1, 5, 2, 3, 2, 3, 1, 2, 2, 2, 2, 2, 1, 4, 1, 2, 3, 2, 2, 3, 1, 3, 2, 3, 1, 3, 1, 2, 3, 3, 2, 3, 1, 5, 4, 2, 1, 4, 2, 2, 2

Offset

1,4

Links

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

Formula

a(n) = A001222(A365296(n)).

Additive with a(p^e) = A006519(e).

a(n) = 1 if and only if n is in A246551.

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{p prime} f(1/p) = 0.42540262231508387576..., where f(x) = -x + (1-x) * Sum_{k>=0} (2^(k+1)-1)*x^(2^k)/(1+x^(2^k)).

Mathematica

f[p_, e_] := 2^IntegerExponent[e, 2]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = vecsum(apply(x -> 2^valuation(x, 2), factor(n)[, 2]));

Crossrefs

Cf. A001222, A006519, A246551, A365296.

Sequence in context: A140192 A324905 A240231 * A065373 A047895 A307322

Adjacent sequences: A366072 A366073 A366074 * A366076 A366077 A366078

Keyword

nonn,easy

Author

Amiram Eldar, Sep 28 2023

Status

approved