A385662 -id:A385662 - cp's OEIS frontend

A386872 Smallest k for which A385662(k) = n, or -1 if no such k exists.

1, 2, 6, 12, 18, 24, 54, 48, 72, 96, 270, 120, 450, 384, 288, 240, 2310, 360, 1890, 480, 1152, 3150, 4050, 720, 2592, 6930, 1800, 1920, 17010, 1440

Offset: 1

Juri-Stepan Gerasimov, Aug 06 2025

Cf. A385729, A385731, A386410, A385318, A385662.

f(n) = sumdiv(n, d, Mod(d, n)^d == Mod(-d, n)^d); \\ A385662
a(n) = my(k=1); while (f(k) != n, k++); k; \\ Michel Marcus, Aug 06 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

A386872 Smallest k for which A385662(k) = n, or -1 if no such k exists.

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