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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
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
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
MATHEMATICA
perfPQ[n_]:=GCD@@FactorInteger[n][[All, 2]]>1; Table[Times@@Select[Divisors[n], perfPQ[#]&], {n, 120}] (* Harvey P. Dale, Mar 07 2024 *)
PROG
(PARI) A183104(n) = { my(m=1); fordiv(n, d, if(ispower(d), m *= d)); m; }; \\ Antti Karttunen, Oct 07 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Dec 25 2010
STATUS
approved