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A229208

Numbers k such that Sum_{j=1..k} sigma(j)^j == 0 (mod k).

1, 2, 9, 55, 758, 16685, 29224, 84293, 87018, 98122

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OFFSET

1,2

COMMENTS

a(8) > 50000.

a(11) > 10^5. - Hiroaki Yamanouchi, Sep 23 2014

LINKS

Table of n, a(n) for n=1..10.

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

CROSSREFS

Cf. A000203, A227427, A227429, A227502, A227848, A229095, A229207, A229209-A229211.

Sequence in context: A109366 A303914 A241457 * A154749 A240562 A091108

Adjacent sequences: A229205 A229206 A229207 * A229209 A229210 A229211

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Sep 16 2013

EXTENSIONS

a(8)-a(10) from Hiroaki Yamanouchi, Sep 23 2014

STATUS

approved

URL: https://oeis.org/A229208

⇱ A229208 - OEIS