cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A181704 Numbers m=2^(t-1)*(2^t-5), where 2^t-5 is prime.

Original entry on oeis.org

12, 88, 1888, 32128, 521728, 8378368, 34359083008, 549753192448, 2251799645913088, 9223372026117357568, 2361183241263023915008, 2596148429267413634121263069790208, 2722258935367507707522529418717050175488
Offset: 1

Views

Author

Vladimir Shevelev, Nov 06 2010

Keywords

Comments

All these numbers are in A181595 because their abundance is 4, a proper divisor of m.

Crossrefs

Cf. A059608, A156560, A181595, A181701, A000396, A181703, A045769

Programs

  • Mathematica
    Rest[2^(#-1) (2^#-5)&/@(Round[N[Log[#+5]/Log[2]]]&/@Select[Table[2^t-5,{t,120}],PrimeQ])] (* Harvey P. Dale, Dec 16 2010 *)

Extensions

571728 replaced with 521728 by R. J. Mathar, Dec 05 2010

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

Original entry on oeis.org

56, 368, 128768, 2087936, 8589344768, 2199013818368, 36893488108764397568, 904625697166532776746648320380374279912262923807289020860114158381451706368
Offset: 1

Views

Author

Vladimir Shevelev, Nov 06 2010

Keywords

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

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

Views

Author

Vladimir Shevelev, Nov 06 2010

Keywords

Comments

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

Crossrefs

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

Views

Author

Vladimir Shevelev, Nov 06 2010

Keywords

Comments

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.

Crossrefs

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

Extensions

Definition simplified and more terms added by R. J. Mathar, Nov 18 2010
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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