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A175069
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a(n) = product of perfect divisors of n / n.
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2
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1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 64, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10
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OFFSET
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1,4
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COMMENTS
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A perfect divisor of n is a divisor d 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) = A175068(n) / n. a(n) > 1 for perfect powers n = A001597(m) for m > 2.
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MATHEMATICA
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Table[Apply[Times, Select[Divisors@ n, Or[# == 1, #^IntegerExponent[n, #] == n] &]]/n, {n, 105}] (* Michael De Vlieger, Nov 21 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); };
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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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