

A183105


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


4



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
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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^(k1)), 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: A085307 A078599 A183103 * A316608 A033031 A134060
Adjacent sequences: A183102 A183103 A183104 * A183106 A183107 A183108


KEYWORD

nonn,look


AUTHOR

Jaroslav Krizek, Dec 25 2010


STATUS

approved



