A350705 Composite numbers that have no Sophie Germain prime and no "safe prime" factors.

169, 221, 247, 289, 323, 361, 403, 481, 527, 559, 589, 629, 703, 731, 793, 817, 871, 923, 949, 961, 1027, 1037, 1139, 1147, 1159, 1207, 1241, 1261, 1273, 1313, 1333, 1339, 1343, 1349, 1369, 1387, 1417, 1501, 1591, 1649, 1651, 1717, 1751, 1781, 1807, 1843, 1849, 1853

Offset

1,1

Comments

Prime factors of the terms have to be in A059500.

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Example

a(2) = 221 = 13 * 17 and {13, 17} are neither in A005384 nor in A005385, but they are in A059500.

Mathematica

Select[Range[2000], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], ! PrimeQ[2*#1 + 1] && ! PrimeQ[(#1 - 1)/2] &] &] (* Amiram Eldar, Feb 15 2022 *)

Prog

(Python)
from sympy import primefactors, isprime
print([n for n in range(2, 1854) if not isprime(n) and all(not isprime(p*2+1) and not isprime((p-1)//2) for p in primefactors(n))])
(PARI) isok(m) = if ((m>1) && !isprime(m), my(f=factor(m)[, 1]); !#select(x->isprime(2*x+1), f) && !#select(x->isprime((x-1)/2), f)); \\ Michel Marcus, Feb 14 2022

Crossrefs

Subsequence of A350704 and A350706.

Cf. A005384, A005385, A053176, A059500.

Sequence in context: A235718 A239724 A038512 * A141075 A124979 A292559

Adjacent sequences: A350702 A350703 A350704 * A350706 A350707 A350708

Keyword

nonn

Author

Karl-Heinz Hofmann, Feb 14 2022

Status

approved