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A227427
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Numbers k such that Sum_{i=1..k} i^sigma(i) == 0 (mod k).
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8
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1^sigma(1) + 2^sigma(2) + ... + 16^sigma(16) + 17^sigma(17) =
1^1 + 2^3 + 3^4 + 4^7 + 5^6 + 6^12 + 7^8 + 8^15 + 9^13 + 10^18 + 11^12 + 12^28 + 13^14 + 14^24 + 15^24 + 16^31 + 17^18 = 21267649601053603536507860737702745369 and 21267649601053603536507860737702745369 / 17 = 1251038211826682560971050631629573257.
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MAPLE
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with(numtheory); ListA227427:=proc(q) local i, n;
for n from 1 to q do if add(i^sigma(i), i=1..n) mod n=0 then print(n);
fi; od; end: ListA227427(10^6);
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MATHEMATICA
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With[{nn=40000}, Transpose[Select[Thread[{Accumulate[Table[n^DivisorSigma[ 1, n], {n, nn}]], Range[nn]}], Divisible[#[[1]], #[[2]]]&]][[2]]] (* Harvey P. Dale, Jun 08 2016 *)
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PROG
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(PARI) isok(k) = sum(i=1, k, Mod(i, k)^sigma(i)) == 0; \\ Michel Marcus, Feb 18 2021
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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