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A135203
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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.
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1
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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
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OFFSET
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1,2
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COMMENTS
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All 3's apart from 1's in positions given by A001108 and 2 for n=24.
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LINKS
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EXAMPLE
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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
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MAPLE
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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);
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Offset and a typo in the definition corrected by Antti Karttunen, Sep 27 2018
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STATUS
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approved
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