A183105 a(n) = product of divisors of n that are not perfect powers.

1, 2, 3, 2, 5, 36, 7, 2, 3, 100, 11, 432, 13, 196, 225, 2, 17, 648, 19, 2000, 441, 484, 23, 10368, 5, 676, 3, 5488, 29, 810000, 31, 2, 1089, 1156, 1225, 7776, 37, 1444, 1521, 80000, 41, 3111696, 43, 21296, 10125, 2116, 47, 497664, 7, 5000, 2601, 35152, 53, 34992, 3025, 307328, 3249, 3364, 59, 11664000000, 61, 3844, 27783, 2, 4225, 18974736, 67, 78608, 4761, 24010000, 71, 13436928

Offset

1,2

Comments

Sequence is not the same as A183103: a(72) = 13436928, A183103(72) = 186624.

Not multiplicative since a(2)*a(3) <> a(6). - R. J. Mathar, Jun 07 2011

Links

Antti Karttunen, Table of n, a(n) for n = 1..16385

Formula

a(n) = A007955(n) / A183104(n).

a(1) = 1, a(p) = p, a(pq) = (pq)^2, a(pq...z) = (pq...z)^(2^(k-1)), a(p^k) = p, 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 {2, 3, 6, 12}; a(12) = 1*2*3*6*12 = 432.

Maple

isA001597 := proc(n) local e ; e := seq(op(2, p), p=ifactors(n)[2]) ; return ( igcd(e) >=2 ) ; end proc:
A183105 := proc(n) local a, d; a := 1 ; for d in numtheory[divisors](n) do if not isA001597(d) then a := a*d; end if; end do; a ; end proc:
seq(A183105(n), n=1..72) ; # R. J. Mathar, Jun 07 2011

Prog

(PARI) A183105(n) = { my(m=1); fordiv(n, d, if(!ispower(d), m *= d)); m; }; \\ Antti Karttunen, Oct 07 2017

Crossrefs

Cf. A001597, A007955, A183101, A183103, A183104.

Sequence in context: A353975 A078599 A183103 * A316608 A033031 A134060

Adjacent sequences: A183102 A183103 A183104 * A183106 A183107 A183108

Keyword

nonn,look

Author

Jaroslav Krizek, Dec 25 2010

Status

approved