A178646 - OEIS

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, 51, 2704, 1, 157464, 55, 175616, 57, 58, 1, 777600000, 1, 62, 3969, 512, 65

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

LINKS

Table of n, a(n) for n=1..65.

FORMULA

a(n) = A007955(n) / A175068(n).

a(1) = 1, a(p) = 1, a(p*q) = p*q, a(p*q*...*z) = (p*q*...*z)^(2^(k-1)-1), for p, q = primes, k = natural numbers, p*q*...*z = product of k (k > 2) distinct primes p, q, ..., z. [corrected by Jason Yuen, Dec 17 2025]

EXAMPLE

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

PROG

(SageMath) 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, A175068.

Sequence in context: A358981 A392411 A160199 * A144540 A292107 A212037

Adjacent sequences: A178643 A178644 A178645 * A178647 A178648 A178649

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Dec 25 2010

EXTENSIONS

More terms from Michel Marcus, Dec 17 2025

STATUS

approved