

A175068


a(n) = product of perfect divisors of n. Perfect divisor of n is divisor d such that d^k = n for some k >= 1.


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(n) > n for perfect powers n = A001597(m) for m > 2.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = A175069(n) * n. [From 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 *)


CROSSREFS

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



