A275493 Number of primitive weird numbers (A002975) below 2^n.

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 6, 8, 9, 10, 14, 16, 20, 24, 29, 33, 46, 55, 61, 79, 87, 103, 128, 152, 173, 234, 266, 313, 403, 483, 561, 756, 850, 940

Offset: 0

Author

M. F. Hasler, Jul 30 2016

Keywords

• nonn
• more

Comments

It is not known unconditionally whether there are infinitely many primitive weird numbers (PWN, A002975), although numerical data provides strong evidence: even the number of weird numbers of the form 2^k*p*q (A258882, A258333) seems to increase rapidly as k increases. Melfi has shown that Cramer's conjecture implies the infiniteness of PWN.

Links

• Giuseppe Melfi, On the conditional infiniteness of primitive weird numbers, Journal of Number Theory, Volume 147, February 2015, Pages 508-514.

Crossrefs

Cf. A002975, A006037, A258333, A258882, A275494, A275491, A275492.

Programs

PARI

vector(40,n,#select(t->t<2^n,A002975)) \\ assuming that A002975 is defined as a set, vector or list with enough terms.

Extensions

a(0) inserted, a(39) corrected, and a(40) added by Amiram Eldar, Sep 02 2023