A181704 -id:A181704 - cp's OEIS frontend

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

Vladimir Shevelev, Nov 06 2010

nonn

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).)

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

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

Edited by R. J. Mathar, Sep 12 2011

A181706 Numbers of the form 2^(t-1)*(2^t-17), where 2^t-17 is prime.

Original entry on oeis.org

1504, 30592, 8353792, 2146926592, 34357510144, 549746900992, 8796057370624, 140737345748992, 9223372000347553792, 2361183240850707054592, 9671406556879650002305024, 154742504910523000781012992

Offset: 1

Vladimir Shevelev, Nov 06 2010

nonn

All entries are near-perfect numbers (A181595). The proof follows as in A181705, but this time the abundance is 16.

Cf. A059611, A181595, A181701, A000396, A181703, A181704, A181705.

A181707 Numbers of the form m=2^(t-1)*(2^t-33), where 2^t-33 is prime.

Original entry on oeis.org

992, 28544, 122624, 507392, 34355412992, 8796023816192, 140737211531264, 144115179217485824, 9671406556844465630216192, 162259276829213066154002603835392, 11417981541647679048463794346093005918389141504

Offset: 1

Vladimir Shevelev, Nov 06 2010

nonn

Generated by t= 6, 8, 9, 10, 18, 22, 24, 29, 42, 54, 77, 90, 102, 137,...

A subsequence of A181595 because the abundance of m is 32, and 32 divides 2^(t-1) and therefore divides m.

Cf. A181595, A181701, A000396, A181703, A181704, A181705, A181706, A175989.

Definition simplified and more terms added by R. J. Mathar, Nov 18 2010

cp's OEIS Frontend

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

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A181706 Numbers of the form 2^(t-1)*(2^t-17), where 2^t-17 is prime.

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A181707 Numbers of the form m=2^(t-1)*(2^t-33), where 2^t-33 is prime.

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