A178646 a(n) = product of divisors d of n such that d^k is not equal to n for any k >= 1.

1, 1, 1, 1, 1, 6, 1, 4, 1, 10, 1, 144, 1, 14, 15, 8, 1, 324, 1, 400, 21, 22, 1, 13824, 1, 26, 9, 784, 1, 27000, 1, 512, 33, 34, 35, 46656, 1, 38, 39, 64000, 1, 74088, 1, 1936, 2025, 46, 1, 5308416, 1, 2500

Offset

1,6

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = A007955(n) / A157068 (n).

a(1) = 1, a(p) = 1, a(pq) = 1, a(pq...z) = (pq…z)^2((k-1)-1), for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.

Example

For n = 16, set of such divisors is {1, 8}; a(16) = 1*8=8.

Prog

(Sage) A178646 = lambda n: prod(d for d in divisors(n) if not n.is_power_of(d)) # D. S. McNeil, Dec 28 2010

Crossrefs

Cf. A007955, A157068.

Sequence in context: A371348 A358981 A160199 * A144540 A292107 A212037

Adjacent sequences: A178643 A178644 A178645 * A178647 A178648 A178649

Keyword

nonn

Author

Jaroslav Krizek, Dec 25 2010

Status

approved