A275492 Number of primitive weird numbers (A002975) between 10^n and 10^(n+1).

0, 1, 1, 5, 6, 11, 24, 37, 67, 124, 223, 382

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, A275491, A275493, A275494.

Programs

PARI

a(n)=sum(n=10^n\2+1,5*10^n,is_A002975(n*2))

Extensions

Wrong initial term removed and a(11) added by Amiram Eldar, Sep 02 2023