A183095 a(n) = number of divisors d of n which are either 1 or of the form Product_(i) (p_i^e_i) where the e_i are <= 1.

1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 5, 2, 4, 4, 2, 2, 5, 2, 5, 4, 4, 2, 6, 2, 4, 2, 5, 2, 8, 2, 2, 4, 4, 4, 6, 2, 4, 4, 6, 2, 8, 2, 5, 5, 4, 2, 7, 2, 5, 4, 5, 2, 6, 4, 6, 4, 4, 2, 11, 2, 4, 5, 2, 4, 8, 2, 5, 4, 8, 2, 7, 2, 4, 5, 5, 4, 8, 2, 7, 2, 4, 2, 11, 4, 4, 4, 6, 2, 11, 4, 5, 4, 4, 4, 8, 2, 5, 5, 6

Offset

1,2

Comments

a(n) = number of non-powerful divisors d of n where powerful numbers are numbers from A001694(m) for m >=1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A000005(n) - A183094(n) = A183093(n) + 1.

a(1) = 1, a(p) = 2, a(pq) = 4, a(pq...z) = 2^k, a(p^k) = 2, 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 {1, 2, 3, 6, 12}; a(12) = 5.

Crossrefs

Cf. A000005, A183093, A183094.

Sequence in context: A318465 A073180 A316398 * A304817 A242802 A277561

Adjacent sequences: A183092 A183093 A183094 * A183096 A183097 A183098

Keyword

nonn

Author

Jaroslav Krizek, Dec 25 2010

Status

approved