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A242899
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Least number k > 1 such that (n^k+k^n)/(k+n) is an integer.
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5
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2, 2, 3, 4, 3, 3, 3, 2, 3, 6, 8, 4, 11, 5, 3, 16, 7, 6, 5, 5, 3, 10, 5, 3, 4, 5, 3, 4, 11, 4, 7, 11, 3, 30, 5, 3, 7, 19, 3, 10, 7, 6, 7, 11, 5, 12, 14, 6, 7, 5, 3, 12, 13, 9, 5, 8, 6, 6, 11, 4, 4, 6, 3, 64, 5, 6, 10, 6, 3, 10, 6, 6, 5, 37, 3, 30, 7, 12, 7, 20, 3, 40, 19, 9
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OFFSET
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1,1
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COMMENTS
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a(n) <= n for all n > 1.
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LINKS
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EXAMPLE
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(1^2+2^1)/(2+1) = 3/3 = 1 is an integer. Thus a(1) = 2.
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MATHEMATICA
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lnk[n_]:=Module[{k=2}, While[!IntegerQ[(n^k+k^n)/(k+n)], k++]; k]; Array[lnk, 90] (* Harvey P. Dale, Sep 02 2015 *)
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PROG
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(PARI) a(n)=if(n==1, 2, for(k=2, n, s=(n^k+k^n)/(k+n); if(floor(s)==s, return(k))))
n=1; while(n<100, print(a(n)); n+=1)
(PARI) a(n) = my(k=2); while (denominator((n^k+k^n)/(k+n))!=1, k++); k; \\ Michel Marcus, Jun 03 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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