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A135203 For any integer n >= 1 the sequence gives the minimum power x for which n^x+(n-1)^x+(n-2)^x+...+1^x produces a perfect square.

%I A135203 #9 Sep 27 2018 17:55:32
%S A135203 1,3,3,3,3,3,3,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,3,3,3,3,3,3,3,3,3,3,
%T A135203 3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%U A135203 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3
%N A135203 For any integer n >= 1 the sequence gives the minimum power x for which n^x+(n-1)^x+(n-2)^x+...+1^x produces a perfect square.
%C A135203 All 3's apart from 1's in positions given by A001108 and 2 for n=24.
%H A135203 Antti Karttunen, <a href="/A135203/b135203.txt">Table of n, a(n) for n = 1..65537</a>
%e A135203 n=4 -> 4^3+3^3+2^3+1^3 = 64+27+8+1 = 100
%e A135203 n=5 -> 5^3+4^3+3^3+2^3+1^3 = 125+64+27+8+1 = 225
%e A135203 n=6 -> 6^3+5^3+4^3+3^3+2^3+1^3 = 216+125+64+27+8+1 = 441
%p A135203 P:=proc(n) local a,i,k,j,ok,x; for i from 1 by 1 to n do x:=1; ok:=1; while ok=1 do a:=0; k:=i; while k>0 do a:=a+k^x; k:=k-1; od; if (trunc(sqrt(a)))^2=a then print(x); ok:=0; else x:=x+1; fi; od; od; end: P(100);
%o A135203 (PARI) A135203(n) = for(x=1,oo,if(issquare(sum(k=1,n,k^x)), return(x))); \\ _Antti Karttunen_, Sep 27 2018
%Y A135203 Cf. A001108.
%K A135203 easy,nonn
%O A135203 1,2
%A A135203 _Paolo P. Lava_ and _Giorgio Balzarotti_, Nov 28 2007
%E A135203 Offset and a typo in the definition corrected by _Antti Karttunen_, Sep 27 2018