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A229208
Numbers k such that Sum_{j=1..k} sigma(j)^j == 0 (mod k).
3
1, 2, 9, 55, 758, 16685, 29224, 84293, 87018, 98122
OFFSET
1,2
COMMENTS
a(8) > 50000.
a(11) > 10^5. - Hiroaki Yamanouchi, Sep 23 2014
EXAMPLE
sigma(1)^1 + sigma(2)^2 + ... + sigma(9)^9 = 13172483385 and 13172483385 / 9 = 1463609265.
MAPLE
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);
MATHEMATICA
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 *)
PROG
(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
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Sep 16 2013
EXTENSIONS
a(8)-a(10) from Hiroaki Yamanouchi, Sep 23 2014
STATUS
approved