A382887 -id:A382887 - cp's OEIS frontend

A382646 Numbers k such that (k2^d - 1)(d*2^k - 1) is semiprime for some divisor d of k.

2, 3, 6, 7, 12, 18, 19, 21, 30, 31, 42, 60, 75, 81, 115, 123, 126, 132, 133, 225, 249, 306, 324, 362, 384, 462, 468, 512, 606, 607, 612, 751, 822, 1279, 2170, 2202, 2281, 5312, 7755, 9531, 12379, 14898, 15822, 18123, 18819, 18885, 22971, 23005, 23208, 41628, 44497, 51384, 52540, 98726

Offset: 1

Juri-Stepan Gerasimov, Apr 01 2025

nonn

No further terms <= 10^5. - Michael S. Branicky, Apr 07 2025

			7 is in this sequence because (7*2^1-1)*(1*2^7-1) = 13*127 is semiprime for divisor 1 of 7.

Supersequence of A002234.

Cf. A001358, A003261, A382887.

[n: n in [1..1000] | not #[d: d in Divisors(n) | IsPrime(d*2^n-1) and IsPrime(n*2^d-1)] eq 0];

isok(k) = fordiv(k, d, if (ispseudoprime(k*2^d - 1) && ispseudoprime(d*2^k - 1), return(1))); \\ Michel Marcus, Apr 02 2025

from itertools import count, islice
from sympy import isprime, divisors
def A382646_gen(): # generator of terms
    yield from filter(lambda k:any(isprime((k<A382646_list = list(islice(A382646_gen(), 30)) # Chai Wah Wu, Apr 15 2025

a(40) from Michel Marcus, Apr 02 2025

a(41)-a(54) from Michael S. Branicky, Apr 07 2025

cp's OEIS Frontend

A382646 Numbers k such that (k2^d - 1)(d*2^k - 1) is semiprime for some divisor d of k.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

PARI

Python

Extensions

cp's OEIS Frontend

A382646 Numbers k such that (k*2^d - 1)*(d*2^k - 1) is semiprime for some divisor d of k.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

PARI

Python

Extensions

A382646 Numbers k such that (k2^d - 1)(d*2^k - 1) is semiprime for some divisor d of k.