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A175069
a(n) = product of perfect divisors of n / n.
2
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
OFFSET
1,4
COMMENTS
A perfect divisor of n is a divisor d such that d^k = n for some k >= 1.
LINKS
FORMULA
a(n) = A175068(n) / n. a(n) > 1 for perfect powers n = A001597(m) for m > 2.
MATHEMATICA
Table[Apply[Times, Select[Divisors@ n, Or[# == 1, #^IntegerExponent[n, #] == n] &]]/n, {n, 105}] (* Michael De Vlieger, Nov 21 2017 *)
PROG
(PARI)
A175068(n) = { my(m=1); fordiv(n, d, if((1==d)||(d^valuation(n, d))==n, m*=d)); (m); };
A175069(n) = (A175068(n)/n); \\ Antti Karttunen, Nov 21 2017
CROSSREFS
Cf. A175068.
Sequence in context: A362414 A245562 A304495 * A245563 A356917 A122945
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 23 2010
STATUS
approved