

A183096


a(n) = number of divisors of n that are not perfect powers.


9



0, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 3, 1, 1, 4, 1, 4, 3, 3, 1, 5, 1, 3, 1, 4, 1, 7, 1, 1, 3, 3, 3, 5, 1, 3, 3, 5, 1, 7, 1, 4, 4, 3, 1, 6, 1, 4, 3, 4, 1, 5, 3, 5, 3, 3, 1, 10, 1, 3, 4, 1, 3, 7, 1, 4, 3, 7, 1, 7, 1, 3, 4, 4, 3, 7, 1, 6, 1, 3, 1, 10, 3, 3, 3, 5, 1, 10, 3, 4, 3, 3, 3, 7, 1, 4, 4, 5
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OFFSET

1,6


COMMENTS

Sequence is not the same as A183093(n): a(72) = 7, A183093(72) = 6.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from exponents in factorization of n


FORMULA

a(n) = A000005(n)  A091050(n).
a(1) = 0, a(p) = 1, a(pq) = 3, a(pq...z) = 2^k  1, a(p^k) = 1, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.


EXAMPLE

For n = 12, set of such divisors is {2, 3, 6, 12}; a(12) = 4.


PROG

(PARI)
A091050(n) = (1+ sumdiv(n, d, ispower(d)>1)); \\ This function from Michel Marcus, Sep 21 2014
A183096(n) = (numdiv(n)  A091050(n)); \\ Antti Karttunen, Nov 23 2017


CROSSREFS

Cf. A000005, A091050, A183093, A183095.
Sequence in context: A095960 A316314 A183093 * A029356 A291448 A114006
Adjacent sequences: A183093 A183094 A183095 * A183097 A183098 A183099


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Dec 25 2010


STATUS

approved



