A181705 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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).)

LINKS

Table of n, a(n) for n=1..8.

MATHEMATICA

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

CROSSREFS