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

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: A277013 A086436 A001222 * A253557 A098893 A069248

Adjacent sequences:  A257088 A257089 A257090 * A257092 A257093 A257094

KEYWORD

nonn

AUTHOR

Wolfgang Hintze, Apr 16 2015

STATUS

approved

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Last modified December 12 16:18 EST 2017. Contains 295939 sequences.