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

0, 0, 1, 2, 7, 13, 24, 48, 85, 152, 277, 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.

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

Prog

(PARI) s=0; vector(22, n, s+=sum(n=10^n\20+1, 10^n\2, is_A002975(n*2)))
(PARI) vector(22, n, #select(t->t<10^n, A002975)) \\ If A002975 is defined as set, vector, or list with enough terms.

Crossrefs

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

Sequence in context: A045377 A180470 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

Status

approved