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A175068
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a(n) = product of perfect divisors of n.
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5
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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
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OFFSET
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1,2
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COMMENTS
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A perfect divisor d of n is a divisor such that d^k = n for some k >= 1.
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LINKS
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FORMULA
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a(n) > n for perfect powers n = A001597(m) for m > 2.
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EXAMPLE
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For n = 8: a(8) = 16; there are two perfect divisors of 8: 2 and 8; their product is 16.
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MAPLE
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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:
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MATHEMATICA
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Table[Times@@Select[Rest[Divisors[n]], IntegerQ[Log[#, n]]&], {n, 70}] (* Harvey P. Dale, May 01 2017 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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