A317299 Semiprimes in A072226.

4, 6, 9, 10, 14, 15, 22, 26, 33, 34, 38, 46, 49, 62, 65, 69, 77, 85, 86, 93, 122, 129, 133, 145, 158, 202, 254, 334, 382, 398, 447, 471, 579, 626, 694, 745, 1402, 1727, 1781, 2353, 3415, 3418, 3481, 3817, 5053, 5234, 5403, 7078, 7617, 8033, 10967, 11581

Offset

1,1

Comments

Semiprimes k such that A019320(k) is prime.

Numbers of the form p^2 where (2^(p^2) - 1)/(2^p - 1) is prime, or numbers of the form p*q where (2^(p*q) - 1)/((2^p - 1)*(2^q - 1)) is prime. Here p and q are necessarily primes.

Links

Jianing Song, Table of n, a(n) for n = 1..78 (using data from A072226)

Example

15 is a semiprime and Phi_15(2) = (2^15 - 1)/((2^3 - 1)*(2^5 - 1)) = 151 is prime, so 15 is a term. Here Phi_n is the n-th cyclotomic polynomial.
49 is a semiprime and Phi_49(2) = (2^49 - 1)/(2^7 - 1) = 4432676798593 is prime, so 49 is a term.

Prog

(PARI) for(k=1, 1000, if(isprime(polcyclo(k, 2))&&bigomega(k)==2, print1(k, ", ")))

Crossrefs

Cf. A019320, A072226.

Sequence in context: A078972 A115652 A337372 * A236026 A193305 A084759

Adjacent sequences: A317296 A317297 A317298 * A317300 A317301 A317302

Keyword

nonn

Author

Jianing Song, Jan 22 2019

Status

approved