A274222 Numbers n = p_1^s_1...p_m^s_m such that n/p_i^s_i == 1 (mod p_i) for all 0<i<=m.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 36, 37, 41, 43, 47, 48, 49, 53, 56, 59, 61, 64, 67, 71, 73, 79, 80, 81, 83, 89, 97, 101, 103, 107, 108, 109, 113, 121, 125, 127, 128, 131, 137, 139, 144, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 192, 193, 197, 199, 211

Offset

1,2

Links

Table of n, a(n) for n=1..71.

Jose María Grau, A. M. Oller-Marcen, Power sums over commutative and unitary rings, arXiv:1603.05787 [math.RA], 2016.

Example

12 = 2^2 * 3 is in the sequence because 12/2^2 = 3 == 1 (mod 2) and 12/3 = 4 == 1 (mod 3). - Michael B. Porter, Jul 24 2016

Mathematica

fa = FactorInteger; test[n_] := Union@Table[Mod[n/fa[n][[i, 1]]^(fa[n][[i, 2]]), fa[n][[ i, 1]]] == 1, {i, Length[fa[n]]}] == {True}; Select[Range[1000], test]

Prog

(PARI) isok(n) = {f = factor(n); for (k=1, #f~, if (n/f[k, 1]^f[k, 2] % f[k, 1] != 1, return (0)); ); 1; } \\ Michel Marcus, Jul 25 2016

Crossrefs

Cf. A266005, A274223.

Sequence in context: A133813 A326836 A326841 * A300273 A353844 A353833

Adjacent sequences: A274219 A274220 A274221 * A274223 A274224 A274225

Keyword

nonn

Author

José María Grau Ribas, Jun 14 2016

Status

approved