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A183104 a(n) = product of divisors of n that are perfect powers. 4
1, 1, 1, 4, 1, 1, 1, 32, 9, 1, 1, 4, 1, 1, 1, 512, 1, 9, 1, 4, 1, 1, 1, 32, 25, 1, 243, 4, 1, 1, 1, 16384, 1, 1, 1, 1296, 1, 1, 1, 32, 1, 1, 1, 4, 9, 1, 1, 512, 49, 25, 1, 4, 1, 243, 1, 32, 1, 1, 1, 4, 1, 1, 9, 1048576, 1, 1, 1, 4, 1, 1, 1, 10368 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Sequence is not the same as A183102: a(72) = 10368, A183102(72) = 746496.

Not multiplicative, as a(4)*a(9) <> a(36). - R. J. Mathar, Jun 07 2011

LINKS

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

FORMULA

a(n) = A007955(n) / A183105(n).

a(1) = 1, a(p) = 1, a(pq) = 1, a(pq...z) = 1, a(p^k) = p^((1/2*k*(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 = 12, set of such divisors is {1, 4}; a(12) = 1*4 = 4.

MAPLE

isA001597 := proc(n) local e ; e := seq(op(2, p), p=ifactors(n)[2]) ; return ( igcd(e) >=2 ) ; end proc:

A183104 := proc(n) local a, d; a := 1 ; for d in numtheory[divisors](n) do if isA001597(d) then a := a*d; end if; end do; a ; end proc:

seq(A183104(n), n=1..72) ; # R. J. Mathar, Jun 07 2011

PROG

(PARI) A183104(n) = { my(m=1); fordiv(n, d, if(ispower(d), m *= d)); m; }; \\ Antti Karttunen, Oct 07 2017

CROSSREFS

Cf. A001597, A007955, A091051, A183102, A183105.

Sequence in context: A203639 A265679 A112622 * A183102 A178649 A119591

Adjacent sequences:  A183101 A183102 A183103 * A183105 A183106 A183107

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Dec 25 2010

STATUS

approved

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Last modified October 14 14:06 EDT 2019. Contains 328017 sequences. (Running on oeis4.)