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 A175068 a(n) = product of perfect divisors of n. 5
 1, 2, 3, 8, 5, 6, 7, 16, 27, 10, 11, 12, 13, 14, 15, 128, 17, 18, 19, 20, 21, 22, 23, 24, 125, 26, 81, 28, 29, 30, 31, 64, 33, 34, 35, 216, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 343, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 4096, 65, 66, 67, 68, 69, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A perfect divisor d of n is a divisor such that d^k = n for some k >= 1. LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 (first 1000 terms from Harvey P. Dale) FORMULA a(n) > n for perfect powers n = A001597(m) for m > 2. a(n) = A175069(n) * n. - Jaroslav Krizek, Jan 24 2010 EXAMPLE For n = 8: a(8) = 16; there are two perfect divisors of 8: 2 and 8; their product is 16. MAPLE A175068 := proc(n) local a, d, k ; if n = 1 then return 1; end if; a := 1 ; for d in numtheory[divisors](n) minus {1} do for k from 1 do if d^k = n then a := a*d ; end if; if d^k >= n then break; end if; end do: end do: a ; end proc: seq(A175068(n), n=1..80) ; # R. J. Mathar, Apr 14 2011 MATHEMATICA Table[Times@@Select[Rest[Divisors[n]], IntegerQ[Log[#, n]]&], {n, 70}] (* Harvey P. Dale, May 01 2017 *) PROG (PARI) A175068(n) = { my(m=1); fordiv(n, d, if((1==d)||(d^valuation(n, d))==n, m*=d)); (m); }; \\ Antti Karttunen, Nov 21 2017 CROSSREFS Cf. A001597, A175069, A175084, A175085, A175087. Sequence in context: A138682 A065632 A242480 * A157488 A188385 A102631 Adjacent sequences:  A175065 A175066 A175067 * A175069 A175070 A175071 KEYWORD nonn AUTHOR Jaroslav Krizek, Jan 23 2010 STATUS approved

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Last modified March 23 04:45 EDT 2018. Contains 301099 sequences. (Running on oeis4.)