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A350704 Composite numbers that have no Sophie Germain prime factors. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

A350705 is a subsequence too.

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

(Python)

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))])

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

CROSSREFS

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

Sequence in context: A231275 A158725 A090825 * A157342 A230226 A178705

Adjacent sequences:  A350701 A350702 A350703 * A350705 A350706 A350707

KEYWORD

nonn

AUTHOR

Karl-Heinz Hofmann, Feb 11 2022

STATUS

approved

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Last modified August 17 16:21 EDT 2022. Contains 356189 sequences. (Running on oeis4.)