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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.
3
1, 3, 5, 7, 11, 13, 17, 19, 21, 23, 29, 31, 35, 37, 39, 41, 43, 47, 53, 55, 57, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 93, 97, 101, 103, 107, 109, 111, 113, 115, 119, 127, 129, 131, 133, 137, 139, 143, 149, 151, 155
OFFSET
1,2
COMMENTS
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, ..., .
LINKS
EXAMPLE
15 is not in the sequence since its two prime factors are 3 and 5, and 5+1 is divisible by 3.
MATHEMATICA
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]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved