A183092 a(n) is the product of divisors d of n such that d is not equal to m^k where m = noncomposite number, k >= 1.

1, 1, 1, 1, 1, 6, 1, 1, 1, 10, 1, 72, 1, 14, 15, 1, 1, 108, 1, 200, 21, 22, 1, 1728, 1, 26, 1, 392, 1, 27000, 1, 1, 33, 34, 35, 46656, 1, 38, 39, 8000, 1, 74088, 1, 968, 675, 46, 1, 82944, 1, 500, 51, 1352, 1, 5832, 55, 21952, 57, 58, 1, 388800000, 1, 62, 1323, 1, 65, 287496, 1, 2312, 69, 343000, 1, 80621568, 1, 74, 1125, 2888, 77

Offset: 1

Author

Jaroslav Krizek, Dec 25 2010

Keywords

• nonn

Comments

For n = 12, the set of such divisors is {6, 12}; a(12) = 6*12 = 72.

a(n) is also the product of divisors d of n such that d is not equal to p^k where p = prime, k >=1. For n = 12, the set of such divisors is {1, 6, 12}; a(12) = 1*6*12 = 72.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A007955, A183091.

Programs

Maple

A183092 := proc(n) local a,d; a := 1 ; for d in numtheory[divisors](n) minus {1} do if nops( numtheory[factorset](d)) > 1 then a := a*d; end if; end do: a ; end proc: # R. J. Mathar, Apr 14 2011

PARI

A183092(n) = factorback(apply(d -> if(isprimepower(d),1,d), divisors(n))); \\ Antti Karttunen, Aug 06 2018

Formula

a(n) = A007955(n) / A183091(n).

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

Extensions

More terms from Antti Karttunen, Aug 06 2018