A350706 -id:A350706 - cp's OEIS frontend

A350704 Composite numbers that have no Sophie Germain prime factors.

49, 91, 119, 133, 169, 217, 221, 247, 259, 289, 301, 323, 329, 343, 361, 403, 413, 427, 469, 481, 497, 511, 527, 553, 559, 589, 611, 629, 637, 679, 703, 707, 721, 731, 749, 763, 767, 793, 799, 817, 833, 871, 889, 893, 923, 931, 949, 959, 961, 973, 1003, 1027, 1037, 1043

Offset: 1

Karl-Heinz Hofmann, Feb 11 2022

nonn

A157342 is a subsequence. First differs at a(14) = 343.

A350705 is a subsequence too.

			a(2) = 91 = 7 * 13 and {7, 13} are not in A005384.

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

Cf. A157342, A005384, A053176, A350705, A350706.

Select[Range[1000], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], !PrimeQ[2*#1 + 1] &] &] (* Amiram Eldar, Feb 12 2022 *)

isok(m) = if ((m>1) && !isprime(m), !#select(x->isprime(2*x+1), factor(m)[,1])); \\ Michel Marcus, Feb 11 2022

from sympy import primefactors, isprime
print([n for n in range(2,1044) if not isprime(n) and all(not isprime(p*2+1) for p in primefactors(n))])

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

Original entry on oeis.org

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

Karl-Heinz Hofmann, Feb 14 2022

nonn

Prime factors of the terms have to be in A059500.

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

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

Subsequence of A350704 and A350706.

Cf. A005384, A005385, A053176, A059500.

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

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

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))])

cp's OEIS Frontend

A350704 Composite numbers that have no Sophie Germain prime factors.

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