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A229208
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Numbers k such that Sum_{j=1..k} sigma(j)^j == 0 (mod k).
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3
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OFFSET
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1,2
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COMMENTS
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a(8) > 50000.
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LINKS
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EXAMPLE
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sigma(1)^1 + sigma(2)^2 + ... + sigma(9)^9 = 13172483385 and 13172483385 / 9 = 1463609265.
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MAPLE
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with(numtheory); P:=proc(q) local n, t; t:=0;
for n from 1 to q do t:=t+sigma(n)^n; if t mod n=0 then print(n);
fi; od; end: P(10^6);
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MATHEMATICA
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Module[{nn=100000}, Select[Thread[{Accumulate[Table[DivisorSigma[1, n]^n, {n, nn}]], Range[nn]}], Divisible[#[[1]], #[[2]]]&]][[All, 2]] (* Harvey P. Dale, Dec 06 2018 *)
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PROG
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(PARI) lista(nn) = {v = vector(nn, i, sigma(i)); for (n=1, nn, if (! sum(i=1, n, Mod(v[i], n)^i), print1(n, ", "); ); ); } \\ Michel Marcus, Sep 21 2013
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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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