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A255602 Numbers k which are odd and squarefree and have the property that k is either a prime number or for every prime p dividing k, p+1 is not divisible by any of the other prime factors of k.

%I A255602 #14 Jan 09 2021 04:45:00
%S A255602 1,3,5,7,11,13,17,19,21,23,29,31,35,37,39,41,43,47,53,55,57,59,61,65,
%T A255602 67,71,73,77,79,83,85,89,93,97,101,103,107,109,111,113,115,119,127,
%U A255602 129,131,133,137,139,143,149,151,155
%N A255602 Numbers k which are odd and squarefree and have the property that k is either a prime number or for every prime p dividing k, p+1 is not divisible by any of the other prime factors of k.
%C A255602 A proper subset of A056911 and a proper subset of A005117. Any divisor of a Lucas-Carmichael number is in this sequence. It is not known whether every number in this sequence divides at least one Lucas-Carmichael number. All prime numbers except 2 are present. Composite numbers in the sequence include 21, 35, 39, 55, 57, 65, 77, 85, 93, 111, 115, 119, 129, 133, 143, 155, 161, 183, 185, 187, ..., .
%H A255602 Amiram Eldar, <a href="/A255602/b255602.txt">Table of n, a(n) for n = 1..10000</a>
%e A255602 15 is not in the sequence since its two prime factors are 3 and 5, and 5+1 is divisible by 3.
%t A255602 fQ[n_] := Block[{fi = FactorInteger@ n}, ffi = First@# & /@ fi; Times @@ (Last@# & /@ fi) == 1 && Min@ Flatten@ Table[ Mod[1 + ffi, i], {i, ffi}] > 0]; fQ[1] = True; fQ[2] = False; Select[ Range@ 190, fQ]
%o A255602 (PARI) isok(n) = {if (! ((n % 2) && issquarefree(n)), return (0)); vpf = factor(n)[, 1]; for (i=1, #vpf, vpx = vpf[i]+1; for (j=1, #vpf, if (! (vpx % vpf[j]), return (0)); ); ); return (1); } \\ _Michel Marcus_, Mar 02 2015
%Y A255602 Cf. A005117, A006972, A056911, A253598.
%K A255602 nonn
%O A255602 1,2
%A A255602 _Tim Johannes Ohrtmann_ and _Robert G. Wilson v_, Feb 27 2015