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.

A072653 Uniqued integer solutions n to n = b^c = c^d.

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%I A072653 #17 Feb 24 2024 01:03:30
%S A072653 1,4,16,27,64,256,729,1024,3125,4096,16384,19683,46656,65536,262144,
%T A072653 531441,823543,1048576,4194304,9765625,14348907,16777216,67108864,
%U A072653 268435456,387420489,1073741824,2176782336,4294967296,10000000000
%N A072653 Uniqued integer solutions n to n = b^c = c^d.
%C A072653 Numbers n such that (n^i)^(n^(1/i)) = (n^j)^(n^(1/j)) for some i and j.
%F A072653 See A072651 for calculation method.
%e A072653 1 is included because of solutions of the form b^0 = 0^0, 1^c = c^0 and 1^1 = 1^d; 4 since 2^2 = 2^2; 16 since 2^4 = 4^2 and 4^2 = 2^4; 27 since 3^3 = 3^3; 64 since 8^2 = 2^6; etc.
%e A072653 The 10th element is n = 4096 with i = 12 and j = 6 because (4096^12)^(4096^(1/12)) = (4096^6)^(4096^(1/6)).
%Y A072653 Cf. A072651, A072652.
%K A072653 nonn
%O A072653 1,2
%A A072653 _Henry Bottomley_, Jun 28 2002
%E A072653 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Oct 07 2006, Jun 05 2007