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

Offset: 1

Author

Paolo P. Lava, Sep 16 2013

Keywords

• nonn
• more

Comments

a(8) > 50000.

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

Examples

			sigma(1)^1 + sigma(2)^2 + ... + sigma(9)^9 = 13172483385 and 13172483385 / 9 = 1463609265.
		

Crossrefs

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

Programs

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 *)

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

Extensions

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