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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
OFFSET
1,1
COMMENTS
Does not include A000312: Number of labeled mappings from n points to themselves (endofunctions): n^n.
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
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