

A188385


Highest power in the prime factorization of n^n


0



0, 2, 3, 8, 5, 6, 7, 24, 18, 10, 11, 24, 13, 14, 15, 64, 17, 36, 19, 40, 21, 22, 23, 72, 50, 26, 81, 56, 29, 30, 31, 160, 33, 34, 35, 72, 37, 38, 39, 120, 41, 42, 43, 88, 90, 46, 47, 192, 98, 100, 51, 104, 53, 162, 55, 168, 57, 58, 59, 120, 61, 62, 126, 384
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..64.


FORMULA

a(n) = n * A051903(n).  Franklin T. AdamsWatters, Mar 29 2011


EXAMPLE

For n = 1, 1^1 = 1, so the highest power in the prime factorization of 1 is a(1) = 0. For n = 12, 12^12 = 8916100448256 = (2^24)(3^12), giving a(12) = 24.


MATHEMATICA

Join[{0}, Table[n*Max[Last /@ FactorInteger[n]], {n, 2, 100}]] (* T. D. Noe, Mar 30 2011 *)


CROSSREFS

Cf. A000312.
Sequence in context: A242480 A175068 A157488 * A102631 A100782 A110340
Adjacent sequences: A188382 A188383 A188384 * A188386 A188387 A188388


KEYWORD

nonn


AUTHOR

A. Timothy Royappa, Mar 29 2011


STATUS

approved



