cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A058125 n^(n^n)/(n^n)^n with 0^0=1.

Original entry on oeis.org

0, 1, 1, 387420489, 3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176
Offset: 0

Views

Author

Henry Bottomley, Nov 10 2000

Keywords

Examples

			a(2)=2^4/4^2=16/16=1. a(3)=3^27/27^3=7625597484987/19683=387420489.

Crossrefs

Cf. A002488, A002489, A058124, A058126.

Formula

a(n) =n^(n^n-n^2) =n^A058126(n) =A002488(n)/A002489(n)

A344919 a(n) = n^n - n*(n + 1) / 2.

Original entry on oeis.org

1, 0, 1, 21, 246, 3110, 46635, 823515, 16777180, 387420444, 9999999945, 285311670545, 8916100448178, 302875106592162, 11112006825557911, 437893890380859255, 18446744073709551480, 827240261886336764024, 39346408075296537575253, 1978419655660313589123789, 104857599999999999999999790
Offset: 0

Views

Author

Peter Luschny, Jun 19 2021

Keywords

Crossrefs

Cf. A000217, A000312, A036679, A058126.

Programs

Formula

a(n) = Product_{j=1..n} n - Sum_{j=1..n} j.
a(n) = A000312(n) - A000217(n).

A362738 a(n) is the least nonnegative integer solution for y such that x > 1 is an integer in the equation n^y*x^n = n^(x^(1/n)).

Original entry on oeis.org

0, 0, 192, 3000, 46440, 823200, 16776704, 387419760, 9999999000, 285311669280, 8916100446528, 302875106590056, 11112006825555272, 437893890380856000, 18446744073709547520, 827240261886336759264, 39346408075296537569592, 1978419655660313589117120, 104857599999999999999992000
Offset: 2

Views

Author

Thomas Scheuerle, May 01 2023

Keywords

Comments

Corresponding solutions for x are 256 (2^(2^3)) at n = 2, 19683 (3^(3^2)) at n = 3 and n^(n^2) for all n > 3.
Further solution pairs are of the form y = n^(n^k) - n^(2+k) and x = n^(n^(1+k)) with k > 0.

Crossrefs

Cf. A000312, A058126, A073084.

Programs

  • PARI
    a(n) = max(0,n^n-n^3)

Formula

E.g.f.: 1/(1 + LambertW(-x)) - x*(1 + 3*x + x^2)*exp(x) + 2*x^2, where LambertW() is the Lambert W-function.
a(n) = n^n - n^3 for n > 2.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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