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A257091
a(n) = log_5 (A256693(n)).
3
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)
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
KEYWORD
nonn
AUTHOR
Wolfgang Hintze, Apr 16 2015
STATUS
approved