A183096 - OEIS

%I #8 Nov 23 2017 20:20:19

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A183096/b183096.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = A000005(n) - A091050(n).

%F 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.

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

%o (PARI)

%o A091050(n) = (1+ sumdiv(n, d, ispower(d)>1)); \\ This function from _Michel Marcus_, Sep 21 2014

%o A183096(n) = (numdiv(n) - A091050(n)); \\ _Antti Karttunen_, Nov 23 2017

%Y Cf. A000005, A091050, A183093, A183095.

%K nonn

%O 1,6

%A _Jaroslav Krizek_, Dec 25 2010