Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #21 Jul 24 2024 18:12:21
%S 1,2,4,6,8,16,18,20,24,32,42,45,54,64,72,96,100,128,162,216,256,272,
%T 288,294,320,342,352,384,486,500,512,600,648,720,832,850,864,1024,
%U 1120,1125,1152,1320,1350,1458,1512,1536,1600,1620,1806,1944,2048,2058,2500,2592,2688,3321,3456,3645,3872,4096,4176,4225,4374,4608,4624,5120,5256
%N Numbers k such that k/p_i^r_i == -1 (mod p_i) for all i = 1,...,m, where k = p_1^r_1 .... p_m^r_m.
%H Amiram Eldar, <a href="/A270140/b270140.txt">Table of n, a(n) for n = 1..1688</a> (terms up to 10^10)
%H Jose María Grau and Antonio M. Oller-Marcen, <a href="http://arxiv.org/abs/1603.05787">Power sums over commutative and unitary rings</a>, arXiv:1603.05787 [math.NT], 2016.
%e 8000 is a term since 8000 = 2^6 * 5^3 and 8000 == -2^6 (mod 2^7) and 8000 == -5^3 (mod 5^4).
%t fa = FactorInteger; mas[1]=True; mas[n_] := Union@Table[Mod[n + fa[n][[i, 1]]^ fa[n][[i,2]], fa[n][[i, 1]]^(fa[n][[i, 2]] + 1)], {i, Length[fa[n]]}] == {0}; Select[Range[10000], mas ]
%o (PARI) is(k) = {my(f = factor(k)); for(i = 1, #f~, if((k / f[i, 1]^f[i, 2] + 1) % f[i, 1], return(0))); 1;} \\ _Amiram Eldar_, Jul 24 2024
%Y Cf. A274222.
%K nonn
%O 1,2
%A _José María Grau Ribas_, Mar 12 2016