A181705 Numbers of the form 2^(t-1)*(2^t-9), where 2^t-9 is prime.

56, 368, 128768, 2087936, 8589344768, 2199013818368, 36893488108764397568, 904625697166532776746648320380374279912262923807289020860114158381451706368

Offset: 1

Author

Vladimir Shevelev, Nov 06 2010

Keywords

• nonn

Comments

Subsequence of A181595.

(Proof: Let m=2^(t-1)*(2^t-9) be the entry. By the multiplicative property of the sigma-function, sigma(m)=(2^t-1)*(2^t-8).

The abundance sigma(m)-2*m is therefore 8, and since all t involved are >=4, 8 is a divisor of m because 8 divides 2^(t-1).)

Crossrefs

Cf. A059610, A181595, A181701, A000396, A181703, A181704

Programs

Mathematica

2^(#-1) (2^#-9)&/@Select[Range[3,130],PrimeQ[2^#-9]&] (* Harvey P. Dale, Oct 24 2011 *)

Extensions

Edited by R. J. Mathar, Sep 12 2011