A275491 Number of primitive weird numbers (A002975) below 10^n.

0, 0, 1, 2, 7, 13, 24, 48, 85, 152, 276, 499, 881

Offset

0,4

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. G. Melfi has shown that Cramer's conjecture implies the infiniteness of PWN.

Partial sums of A275492.

Links

Table of n, a(n) for n=0..12.

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

Prog

(PARI) my(s=0); vector(10, n, s+=sum(n=10^n\20+1, 10^n\2, is_A002975(n*2)))
(PARI) vector(10, n, #select(t->t<10^n, A002975)) \\ If A002975 is defined as set, vector, or list with enough terms.

Crossrefs

Cf. A002975, A006037, A258333, A258882, A275492, A275493, A275494.

Sequence in context: A180470 A237443 A182415 * A360673 A183435 A360385

Adjacent sequences: A275488 A275489 A275490 * A275492 A275493 A275494

Keyword

nonn,more

Author

M. F. Hasler, Jul 30 2016

Extensions

a(12) from Robert G. Wilson v, May 25 2018

a(10) corrected by Amiram Eldar, Sep 02 2023

Status

approved