A183093 a(1) = 0; thereafter, a(n) = number of divisors d of n such that if d = Product_(i) (p_i^e_i) then all e_i <= 1.

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, 6, 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

Offset

1,6

Comments

a(n) = number of non-powerful divisors d of n where powerful numbers are numbers from A001694(m) for m >=2.

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

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) - A005361(n) = A183095(n) - 1.

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

(Scheme) (define (A183093 n) (- (A000005 n) (A005361 n))) ;; Antti Karttunen, Nov 23 2017

Crossrefs

Cf. A000005, A005361, A183094, A183095, A183096.

Sequence in context: A372720 A095960 A316314 * A183096 A029356 A334019

Adjacent sequences: A183090 A183091 A183092 * A183094 A183095 A183096

Keyword

nonn

Author

Jaroslav Krizek, Dec 25 2010

Status

approved