A371884 Irregular triangle read by rows in which row n >= 2 lists the divisors d of n such that d^n mod n = d.

1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 5, 1, 1, 4, 1, 1, 7, 1, 5, 1, 1, 1, 9, 1, 1, 5, 1, 7, 1, 11, 1, 1, 1, 1, 13, 1, 1, 4, 1, 1, 6, 10, 15, 1, 1, 1, 11, 1, 17, 1, 1, 9, 1, 1, 19, 1, 13, 1, 1, 1, 7, 21, 1, 1, 1, 9, 1, 23, 1, 1, 16, 1, 1, 25, 1, 17, 1, 13, 1, 1, 27, 1, 11, 1, 8, 1, 19, 1, 29, 1, 1, 1, 1, 31, 1, 1, 1, 5, 13

Offset: 2

Author

Juri-Stepan Gerasimov, Apr 10 2024

Keywords

• nonn
• tabf
• look

Examples

			Triangle begins:
    1;
    1;
    1;
    1;
    1, 3;
    1;
    1;
    1;
    1, 5;
    1;
    1, 4;
    1;
    1, 7;
    1, 5;
    1;
    1;
    1, 9;
    1;
    1, 5;
    1, 7;
    1, 11;
    1;
    1;
    1;
    1, 13;
    1;
    1, 4;
    1;
    1, 6, 10, 15;
    ...
		

Links

• Robert Israel, Table of n, a(n) for n = 2..18962 (rows 2 to 10000, flattened)

Crossrefs

Cf. A027750, A182816, A279024, A371513, A371883.

Programs

Magma

[[d: d in Divisors(n) | d^n mod n eq d]: n in [2..65]];

Maple

f:= proc(n) op(sort(convert(select(d -> d^n mod n = d, numtheory:-divisors(n)),list))) end proc:
for n from 2 to 100 do f(n) od; # Robert Israel, May 11 2025

Mathematica

row[n_] := Select[Divisors[n], PowerMod[#, n, n] == # &]; Array[row, 64, 2] // Flatten (* Amiram Eldar, Apr 11 2024 *)