A386930 -id:A386930 - cp's OEIS frontend

A386284 Smallest k for which A386930(k) = n.

1, 2, 4, 8, 18, 45, 36, 90, 72, 108, 144, 315, 216, 540, 576, 432, 648, 1350, 864, 2160, 1296, 1728, 4050, 2700, 2592, 3888, 6912, 11340, 5184, 5400, 7776, 10395, 10368, 13500, 20790, 10800, 23328, 24300, 16200, 31185, 31104, 21600, 27000, 40500, 62208, 56700

Offset: 1

Juri-Stepan Gerasimov, Aug 14 2025

Cf. A385638, A386930.

a386930[n_] := DivisorSum[n, 1 &, PowerMod[-#, #, n] == Mod[-PowerMod[#, #, n], n] &];a[n_]:=Module[{k=0},Until[a386930[k]==n,k++];k];Array[a,46] (* James C. McMahon, Aug 21 2025 *)

A386310 Number of divisors d of n such that 2*d^d == 0 (mod n).

Original entry on oeis.org

1, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 2, 1, 3, 1, 4, 1, 2, 1, 2, 1, 3, 2, 2, 3, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 2, 2, 1, 4, 2, 4, 1, 2, 1, 6, 1, 3, 1, 2, 1, 2, 1, 2, 2, 5, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 2, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 3, 1, 4, 1, 2, 1, 2, 1, 5, 1, 4, 2, 4

Offset: 1

Juri-Stepan Gerasimov, Aug 20 2025

Cf. A000005, A385429, A385662, A386930.

[1 + #[d: d in [1..n-1] | n mod d eq 0 and Modexp(d,d,n) eq -Modexp(d,d,n) mod n]: n in [1..100]];

Table[Length[Select[Divisors[n], PowerMod[#, #, n] == Mod[n - PowerMod[#, #, n], n] &]], {n, 1, 100}] (* Vaclav Kotesovec, Aug 23 2025 *)

a(n) = sumdiv(n, d, 2*Mod(d, n)^d == 0); \\ Michel Marcus, Aug 30 2025

cp's OEIS Frontend

A386284 Smallest k for which A386930(k) = n.

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