A270140 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.

1, 2, 4, 6, 8, 16, 18, 20, 24, 32, 42, 45, 54, 64, 72, 96, 100, 128, 162, 216, 256, 272, 288, 294, 320, 342, 352, 384, 486, 500, 512, 600, 648, 720, 832, 850, 864, 1024, 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

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..1688 (terms up to 10^10)

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

Example

8000 is a term since 8000 = 2^6 * 5^3 and 8000 == -2^6 (mod 2^7) and 8000 == -5^3 (mod 5^4).

Mathematica

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 ]

Prog

(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

Crossrefs

Cf. A274222.

Sequence in context: A068902 A269332 A077569 * A333020 A325792 A325780

Adjacent sequences: A270137 A270138 A270139 * A270141 A270142 A270143

Keyword

nonn

Author

José María Grau Ribas, Mar 12 2016

Status

approved