A094289 -id:A094289 - cp's OEIS frontend

A113853 Numbers whose prime factors are raised to the powers of themselves.

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

Offset: 1

Cino Hilliard, Jan 25 2006

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

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

Cf. A000312, A048102, A051674, A094289.

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

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

Corrected and extended by Robert G. Wilson v, Jan 26 2006

Offset corrected and more terms added by Amiram Eldar, Oct 13 2020

A370697 Decimal expansion of Sum_{p prime} 1/p!^p.

Original entry on oeis.org

2, 5, 4, 6, 2, 9, 6, 2, 9, 6, 6, 9, 8, 1, 7, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 3, 2, 2, 7, 0, 2, 0, 6, 9, 7, 0, 4, 2, 4, 0, 9, 9, 9, 7, 8, 9, 1, 3, 1, 4, 2, 1, 7, 8, 4, 3, 7, 9, 8, 4, 7, 6, 6, 1, 9, 0, 3, 8, 2, 0, 1, 4, 7, 3, 2, 7, 7, 3, 1, 5, 1, 7, 5, 6, 8, 4, 8, 6, 6, 4, 0, 4, 9, 8, 2, 3, 7, 2

Offset: 0

Roberto Trocchi, Jun 07 2024

			0.25462962966981738683127573227020697042409997891314217843798476619...

Cf. A068210, A100124, A094289, A073009.

RealDigits[Sum[1/Prime[n]!^Prime[n], {n, 1, 12}], 10, 1000] // First

suminf(k=1,1/prime(k)!^prime(k)) \\ Hugo Pfoertner, Jun 22 2024

cp's OEIS Frontend

A113853 Numbers whose prime factors are raised to the powers of themselves.

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