A257091 a(n) = log_5 (A256693(n)).

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 6, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 7, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 5, 4, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 3, 2, 2, 2, 7, 1, 3, 3, 4

Offset

1,4

Comments

a(n) is the logarithm to the base 5 of the denominator of the Dirichlet series of zeta(s)^(1/5). For details, see A256693.

Links

Robert Israel and Wolfgang Hintze, Table of n, a(n) for n = 1..10000 (up to 500 from Wolfgang Hintze)

MathOverflow, The number of prime factors of a natural number.

Formula

5^a(n) = A256693(n).

For n<=10000, if n = Product_i p_i^(e_i) is the prime factorization of n, a(n) = A001222(n) + Sum_i floor(e_i/5). - Robert Israel, May 13 2016

If n = Product_i p_i^(e_i) is the prime factorization of n, a(n) = Sum_{j >= 0} Sum_i floor(e_i/5^j). - Robert Israel, May 16 2016

Maple

F:= proc(n) local e, m;
add(add(floor(e/5^m), m=0..floor(log[5](e))), e=map(t-> t[2], ifactors(n)[2]));
end proc:
seq(F(i), i=1..100);

Mathematica

F[n_] := Sum[Sum[Floor[e/5^m], {m, 0, Floor[Log[5, e]]}], {e, FactorInteger[n][[All, 2]]}];
F[1] = 0;
Array[F, 100] (* Jean-François Alcover, Jun 18 2020, after Maple *)

Crossrefs

Cf. A046645 (k = 2, log_2), A257089 (k = 3, log_3), A257090 (k = 4, log_2), A257091 (k = 5, log_5).

Sequence in context: A326190 A086436 A001222 * A351418 A359909 A319269

Adjacent sequences: A257088 A257089 A257090 * A257092 A257093 A257094

Keyword

nonn

Author

Wolfgang Hintze, Apr 16 2015

Status

approved