A386856 Least k such that A056100(k) = 2*n+1 or -1 if no such k exists.

6, 4, 8, 9, 16, 26, 15, 34, 20, 27, 25, 115, 56, 58, 62, 57, 35, 74, 90, 82, 86, 49, 94, 329, 60, 106, 517582, 78, 91, 122, 110, 77, 128, 111, 142, 146, 88, 427, 158, 102, 100, 265, 273, 178, 242, 95, 212, 194, 104, 202, 125, 462, 214, 218, 132, 121, 344, 138, 470, 241582

Offset: 0

Author

Michel Marcus, Aug 05 2025

Keywords

• nonn

Comments

a(n) is the least k such that (sigma(k)*phi(k) + 1) mod k = 2*n+1 or -1 if no such k exists.

Links

• Michel Marcus, Table of n, a(n) for n = 0..465

Crossrefs

Cf. A056100.

Programs

Mathematica

a[n_]:=Module[{k=1},While[Mod[DivisorSigma[1,k]EulerPhi[k]+1,k]!=2n+1, k++]; k]; Array[a,60,0] (* Stefano Spezia, Aug 05 2025 *)

PARI

f(n) = (sigma(n)*eulerphi(n)+1) % n; \\ A056100
a(n) = my(k=1); while (f(k) != 2*n+1, k++); k;