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.

A273279 Least perfect power that is the sum of two nonzero squares in exactly n ways.

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%I A273279 #15 May 22 2016 00:14:19
%S A273279 8,125,3125,4225,1953125,48828125,105625,274625,762939453125,2640625,
%T A273279 476837158203125,17850625,1221025,34328125,186264514923095703125,
%U A273279 1650390625,446265625,1160290625,41259765625,4291015625,45474735088646411895751953125,30525625
%N A273279 Least perfect power that is the sum of two nonzero squares in exactly n ways.
%C A273279 Least m^k that is the sum of two nonzero squares in exactly n ways where m > 0 and k >= 2.
%C A273279 Terms of this sequence are 2^3, 5^3, 5^5, 65^2, 5^10, 5^11, 325^2, 65^3, ...
%C A273279 Prime powers that are listed in this sequence are 2^3, 5^3, 5^5, 5^10, 5^11, ...
%H A273279 Giovanni Resta, <a href="/A273279/b273279.txt">Table of n, a(n) for n = 1..100</a>
%e A273279 8 is a term because 8 = 2^3 = 2^2 + 2^2.
%e A273279 125 is a term because 125 = 5^3 = 2^2 + 11^2 = 5^2 + 10^2.
%e A273279 3125 is a term because 3125 = 5^5 = 10^2 + 55^2 = 25^2 + 50^2 = 38^2 + 41^2.
%t A273279 p = Select[Prime@ Range@ 90, Mod[#, 4] == 1 &]; f[w_] := Times @@ (Take[p, Length@w]^Reverse[w]); c[w_] := Floor[(1/2) Times @@ (w+1)];r[w_] := Block[{v, k = If[Length@w == 1, 1,2]}, While[(v = cn[k w]) < trg, k++]; If[v == trg, b = Min[b, f[k*w]]]; If[cn[w] < trg, r[Append[w, 1]]; v=w; v[[-1]]++; r[v]]]; a[1]=8; a[n_] := (b=Infinity; trg = n; r[{2}]; r[{1, 1}]; b); Array[a, 50] (* _Giovanni Resta_, May 19 2016 *)
%Y A273279 Cf. A001597, A006339, A016032, A025426, A266927, A273238.
%K A273279 nonn
%O A273279 1,1
%A A273279 _Altug Alkan_, May 19 2016
%E A273279 a(9)-a(22) from _Giovanni Resta_, May 19 2016