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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 21:57 EST 2022. Contains 358453 sequences. (Running on oeis4.)