A231811 Numbers n such that p-1 divides n+1 for every prime divisor p of n.

1, 2, 3, 4, 8, 9, 15, 16, 27, 32, 35, 64, 75, 81, 99, 128, 135, 243, 255, 256, 375, 455, 512, 539, 675, 729, 783, 875, 1024, 1089, 1215, 1295, 1715, 1859, 1875, 2048, 2115, 2187, 2375, 2703, 2975, 3375, 3519, 4096, 4335, 4355, 5375, 5915, 6075, 6479, 6561, 6723

Offset

1,2

Comments

Numbers of the form 2^k, k >= 0, and 3*5^m, m >= 0, are terms. - Marius A. Burtea, Oct 02 2019

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

fa = FactorInteger; Gu[n_] := Union@Table[IntegerQ[(n + 1)/(fa[n][[i, 1]] - 1)], {i, Length[fa[n]]}]; Select[Range[20000], Gu[#] == {True} &]

Prog

(PARI) isok(n) = {my(f=factor(n)[, 1]); for (k=1, #f~, if ((n+1) % (f[k]-1), return(0)); ); return(1); } \\ Michel Marcus, Oct 02 2019
(Magma) [1] cat [k: k in [2..7000]| #[p:p in PrimeDivisors(k)| IsIntegral((k+1)/(p-1))] eq #PrimeDivisors(k)]; // Marius A. Burtea, Oct 02 2019

Crossrefs

Cf. A231810.

Sequence in context: A057844 A281089 A242333 * A015922 A212255 A078829

Adjacent sequences: A231808 A231809 A231810 * A231812 A231813 A231814

Keyword

nonn

Author

José María Grau Ribas, Jan 20 2014

Extensions

Term 1 prepended by Max Alekseyev, Jan 20 2014

Status

approved