A386871 Least k such that A056100(k) = n or -1 if no such k exists.

6, 124357252657, 4, 33, 8, 145, 9, 37063859, 16, 51, 26, 1441, 15, 2353, 34, 69, 20, 1011377103546119, 27, 7201, 25, 87, 115, 9911837, 56, 385, 58, 45, 62, 86125529, 57, 30721, 35, 123, 74, 295, 90, 15686608811, 82, 141, 86, 70561, 49, 77857739, 94, 159, 329, 34884199

Offset: 1

Author

Michel Marcus, Aug 06 2025

Keywords

• nonn
• hard

Comments

Wanted terms: a(18), a(38), a(72), a(80).

a(38) = 15686608811 (found by Tomas Rokicki), a(80) = 4222433393407, and a(18), a(72) > 6*10^12. - Giovanni Resta, Aug 09 2025

a(72) > a(18). - Martin Ehrenstein, Aug 10 2025

Links

• Michel Marcus, Extension to A056100, Seqfan, Aug 05 2025.
• Neil Sloane, Smallest inverse to f(n) = phi(n)*sigma(n) + 1 mod n ?, Math Fun, Aug 05 2025.

Crossrefs

Cf. A056100, A386856 (odd bisection), A015706.

Programs

Mathematica

a[n_]:=Module[{k=0},Until[Mod[DivisorSigma[1, k]*EulerPhi[k] + 1, k]==n,k++];k] (* James C. McMahon, Aug 06 2025 *)

Extensions

a(2) from Tomas Rokicki, Aug 05 2025

a(18) from Martin Ehrenstein, Aug 10 2025

a(19)-a(37) from Hugo Pfoertner, Aug 11 2025

a(38) from Tomas Rokicki, Aug 09 2025

More terms from Hugo Pfoertner, Aug 11 2025