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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.
5
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.
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Dec 25 2010
STATUS
approved