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

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

Partial sums of A275492.

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, A275492, A275493, A275494.

Programs

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.

Extensions

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

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