A317480 Numbers m such that Sum_{k=1..m} 1/gcd(k,m) is an integer.

1, 614341, 618233, 1854699, 11746427, 26584019, 35239281, 79752057, 85393399, 118082503, 345592247, 354247509, 505096361, 802597537, 1036776741, 1062742527, 1515289083, 2149579159, 2243567557, 3695178641, 5077547629, 5250772527, 6566252693, 6730702671

Offset: 1

Author

Amiram Eldar, Jul 29 2018

Keywords

• nonn

Comments

Also numbers n such that n | A057660(n).

a(1)-a(21) are taken from De Koninck's book.

References

• Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, page 265.

Crossrefs

Cf. A057660.

Programs

Mathematica

fun[p_, e_]:=(p^(2e+1)+1)/(p+1); aQ[n_] := Divisible[Times @@ (fun @@@ FactorInteger[n]), n]; Select[Range[10000000], aQ]

PARI

xi(n) = {f = factor(n); for (i=1, #f~, p = f[i, 1]; e = f[i, 2]; f[i, 1] = (p^(2*e+1)+1)/(p+1); f[i, 2] = 1; ); factorback(f); } for(n=1, 1e7, if(xi(n) % n == 0, print(n)))