

A113853


Numbers whose prime factors are raised to the powers of themselves.


0



108, 12500, 84375, 337500, 3294172, 22235661, 88942644, 2573571875, 10294287500, 69486440625, 277945762500, 1141246682444, 7703415106497, 30813660425988, 891598970659375, 1211500426369012, 3566395882637500, 8177627877990831, 24073172207803125, 32710511511963324
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OFFSET

1,1


COMMENTS

Does not include A000312: Number of labeled mappings from n points to themselves (endofunctions): n^n.


LINKS

Table of n, a(n) for n=1..20.


FORMULA

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/p^p)  Sum_{p prime} 1/p^p  1 = 0.009354434361...  Amiram Eldar, Oct 13 2020


EXAMPLE

108 = 2^2*3^3. 2 is raised to the power of itself and 3 is raised to the power of itself.


MATHEMATICA

p = Drop[Subsets@Prime@Range@7, 8]; Take[ Sort[Times @@@ (p^p)], 18] (* Robert G. Wilson v, Jan 26 2006 *)


CROSSREFS

Cf. A000312, A048102, A051674, A094289.
Sequence in context: A273439 A164748 A269093 * A209043 A269272 A209015
Adjacent sequences: A113850 A113851 A113852 * A113854 A113855 A113856


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, Jan 25 2006


EXTENSIONS

Corrected and extended by Robert G. Wilson v, Jan 26 2006
Offset corrected and more terms added by Amiram Eldar, Oct 13 2020


STATUS

approved



