A072808 Smallest m such that sigma(m) == n (mod phi(m)) or 0 if no solution exists.

4, 5, 8, 24, 0, 22, 16, 21, 450, 40, 25, 48, 50, 136, 32, 110, 100, 90, 144, 88, 0, 656, 121, 102, 0, 80, 169, 96, 0, 68, 64, 55, 676, 464, 289, 65, 0, 117, 162, 91, 0, 116, 225, 85, 0, 272, 529, 95, 0, 148, 288, 133, 0, 164, 0, 115, 0, 160, 841, 147, 0, 333, 128, 247

Offset

1,1

Comments

Warning: It is only conjectured that there are no solutions for n such that a(n) = 0. The search for solutions tested all m <= 10^10 for these n.

For odd remainders a(n) is a square or twice a square. See A028982, except terms 1 and 2.

All zeros corresponding to odd terms a(n) with n < 64 confirmed up to m <= 10^24. - Giovanni Resta, Apr 02 2020

Links

Table of n, a(n) for n=1..64.

Formula

a(n) = Min{x; Mod(A000203(x), A000010(x))=n} or 0 if apparently no solutions.

Example

For n=4: a(4)=24 since sigma(24)=60, phi(24)=8 and Mod(60, 8)=4.

Mathematica

f[x_] := Mod[DivisorSigma[1, x], EulerPhi[x]] t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10000000000}];

Crossrefs

Cf. A000203, A000010, A028982, A063514, A067192, A067193, A071390.

Sequence in context: A171938 A325878 A352396 * A104884 A226795 A113726

Adjacent sequences: A072805 A072806 A072807 * A072809 A072810 A072811

Keyword

nonn

Author

Labos Elemer, Jul 12 2002

Status

approved