A274222 - OEIS

%I #24 Jul 24 2024 18:02:18

%S 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,

%T 47,48,49,53,56,59,61,64,67,71,73,79,80,81,83,89,97,101,103,107,108,

%U 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

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

%H Amiram Eldar, <a href="/A274222/b274222.txt">Table of n, a(n) for n = 1..10000</a>

%H Jose María Grau, Antonio M. Oller-Marcen, <a href="http://arxiv.org/abs/1603.05787">Power sums over commutative and unitary rings</a>, arXiv:1603.05787 [math.RA], 2016.

%e 12 = 2^2 * 3 is a term because 12/2^2 = 3 == 1 (mod 2) and 12/3 = 4 == 1 (mod 3). - _Michael B. Porter_, Jul 24 2016

%t 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]

%o (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

%Y Cf. A266005, A270140, A274223.

%K nonn

%O 1,2

%A _José María Grau Ribas_, Jun 14 2016