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.

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, 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, 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

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 28 2007

Keywords

• easy
• nonn

Comments

All 3's apart from 1's in positions given by A001108 and 2 for n=24.

Examples

			n=4 -> 4^3+3^3+2^3+1^3 = 64+27+8+1 = 100
n=5 -> 5^3+4^3+3^3+2^3+1^3 = 125+64+27+8+1 = 225
n=6 -> 6^3+5^3+4^3+3^3+2^3+1^3 = 216+125+64+27+8+1 = 441
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A001108.

Programs

Maple

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);

PARI

A135203(n) = for(x=1,oo,if(issquare(sum(k=1,n,k^x)), return(x))); \\ Antti Karttunen, Sep 27 2018

Extensions

Offset and a typo in the definition corrected by Antti Karttunen, Sep 27 2018