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.

A153474 Sum of first n Mersenne primes A000668.

Original entry on oeis.org

3, 10, 41, 168, 8359, 139430, 663717, 2148147364, 2305843011361841315, 618970021948533148811403426, 162259895799235311924726821691553, 170141345720365030966999228442705797280
Offset: 1

Views

Author

Omar E. Pol, Dec 27 2008

Keywords

Crossrefs

Programs

  • Mathematica
    Accumulate[2^MersennePrimeExponent[Range[15]]-1] (* Harvey P. Dale, Feb 28 2023 *)

Extensions

More terms from Max Alekseyev, Apr 13 2009

A153475 Sum of the first n even superperfect numbers (A061652).

Original entry on oeis.org

2, 6, 22, 86, 4182, 69718, 331862, 1074073686, 1152921505680920662, 309485010974266574405701718, 81129947899617655962363410845782, 85070672860182515483499614221352898646
Offset: 1

Views

Author

Omar E. Pol, Dec 27 2008

Keywords

Comments

Also, sum of first n superperfect numbers A019279, if there are no odd superperfect numbers.

Crossrefs

Formula

a(n) = A061652(1) + A061652(2) + ... + A061652(n). - Max Alekseyev, Jul 27 2009

Extensions

More terms from Max Alekseyev, Jul 27 2009

A153487 Sum of first n perfect numbers A000396, divided by 2.

Original entry on oeis.org

3, 17, 265, 4329, 16779497, 4311714025, 73031059689, 1152921577101035753, 1329227995784915873480267885077956841, 95780971304118054976624684827067692545766545852041449
Offset: 1

Views

Author

Omar E. Pol, Dec 27 2008

Keywords

Comments

Partial sums of A133028. [From R. J. Mathar, Jan 21 2009]

Crossrefs

Programs

  • Mathematica
    Accumulate[(# (#+1))/2&/@Select[2^Range[90]-1,PrimeQ] ]/2 (* Harvey P. Dale, Sep 04 2014 *)

Formula

a(n) = A092336(n)/2.

Extensions

More terms from R. J. Mathar, Jan 21 2009

A178062 Triangle t(n,m) = -A000396(n)+A000396(m)+A000396(n-m) read by rows.

Original entry on oeis.org

1, 1, 1, 1, -16, 1, 1, -462, -462, 1, 1, -7626, -8072, -7626, 1, 1, -33542202, -33549812, -33549812, -33542202, 1, 1, -8556318714, -8589860900, -8589868064, -8589860900, -8556318714, 1, 1, -128848822266, -137405140964, -137438682704
Offset: 0

Views

Author

Roger L. Bagula, May 18 2010

Keywords

Comments

The definition is based on the definition of a perfect number A000396(0) = 1.
Row sums are 1, 2, -14, -922, -23322, -134184026, ... = 2*(A092336(n)+1) -(n+1)*A000396(n). - R. J. Mathar, Nov 26 2010

Examples

			1;
1, 1;
1, -16, 1;
1, -462, -462, 1;
1, -7626, -8072, -7626, 1;
1, -33542202, -33549812, -33549812, -33542202, 1;
1, -8556318714, -8589860900, -8589868064, -8589860900, -8556318714, 1;
1, -128848822266, -137405140964, -137438682704, -137438682704, -137405140964, -128848822266, 1;
1, -2305842870701260794, -2305842999550083044, -2305843008106401296, -2305843008139935872, -2305843008106401296, -2305842999550083044, -2305842870701260794, 1;
		

Crossrefs

Cf. A000396.

Programs

  • Mathematica
    a={1,6,28,496,8128,33550336, 8589869056,137438691328,2305843008139952128,
    2658455991569831744654692615953842176, 191561942608236107294793378084303638130997321548169216}
    t[n_,m_]:=(-a[[n+1]]+(a[[m+1]]+a[[n-m+1]]));
    Table[Table[t[n,m],{m,0,n}],{n,0,10}];
    Flatten[%]

Formula

t(n,m) = t(n,n-m).
Showing 1-4 of 4 results.