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.

Previous Showing 11-15 of 15 results.

A168014 Sum of all parts of all partitions of n into equal parts that do not contain 1 as a part.

Original entry on oeis.org

0, 0, 2, 3, 8, 5, 18, 7, 24, 18, 30, 11, 60, 13, 42, 45, 64, 17, 90, 19, 100, 63, 66, 23, 168, 50, 78, 81, 140, 29, 210, 31, 160, 99, 102, 105, 288, 37, 114, 117, 280, 41, 294, 43, 220, 225, 138, 47, 432, 98, 250, 153, 260, 53, 378
Offset: 0

Views

Author

Omar E. Pol, Nov 20 2009

Keywords

Comments

Sum of all the parts in the partitions of n into two parts such that the smaller part divides the larger. - Wesley Ivan Hurt, Dec 22 2017

Links

Crossrefs

Cf. A000005, A000041, A032741, A168015, A168020, A168021.

Programs

Formula

a(n) = n * A032741(n).
a(n) = n(d(n) - 1) = n*(A000005(n) - 1) = A038040(n) - n, if n >= 1. - Omar E. Pol, Jan 18 2013

Extensions

a(14)-a(55) from Vincenzo Librandi, May 25 2010
New name from Omar E. Pol, Jan 18 2013

A168015 a(n) = A000041(n) + n*A032741(n).

Original entry on oeis.org

1, 1, 4, 6, 13, 12, 29, 22, 46, 48, 72, 67, 137, 114, 177, 221, 295, 314, 475, 509, 727, 855, 1068, 1278, 1743, 2008, 2514, 3091, 3858, 4594, 5814, 6873, 8509, 10242, 12412, 14988, 18265, 21674, 26129, 31302, 37618, 44624, 53468, 63304, 75395, 89359
Offset: 0

Views

Author

Omar E. Pol, Nov 20 2009

Keywords

Links

Crossrefs

Cf. A000005, A032741, A000041, A168014, A168020, A168021.

Programs

  • Mathematica
    Table[PartitionsP[n] + n*(DivisorSigma[0, n] - 1), {n, 0, 50}] (* G. C. Greubel, Jul 05 2016 *)
  • PARI
    a(n) = if (n, numbpart(n) + n*(numdiv(n)-1), numbpart(0)); \\ Michel Marcus, Jul 06 2016

Extensions

a(14)-a(46) from Vincenzo Librandi, May 26 2010

A168120 Square array T(n,k) read by antidiagonals in which column k lists each number A000009 followed by k-1 zeros, for k>0.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 2, 1, 0, 1, 2, 0, 0, 0, 1, 3, 1, 1, 0, 0, 1, 4, 0, 0, 0, 0, 0, 1, 5, 2, 0, 1, 0, 0, 0, 1, 6, 0, 1, 0, 0, 0, 0, 0, 1, 8, 2, 0, 0, 1, 0, 0, 0, 0, 1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 3, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
Offset: 0

Views

Author

Omar E. Pol, Nov 26 2009

Keywords

Comments

The same structure of the square array in A168019, but using the numbers A000009.

Examples

			The array begins:
==================================================
... Column k: 1. 2. 3. 4. 5. 6. 7. 8. 9 10 11 12
. Row ...........................................
...n ............................................
==================================================
.. 0 ........ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
.. 1 ........ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
.. 2 ........ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
.. 3 ........ 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
.. 4 ........ 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
.. 5 ........ 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
.. 6 ........ 4, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
.. 7 ........ 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
.. 8 ........ 6, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0,
.. 9 ........ 8, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0,
. 10 ....... 10, 3, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0,
. 11 ....... 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
. 12 ....... 15, 4, 2, 2, 0, 1, 0, 0, 0, 0, 0, 1,
...

Crossrefs

Cf. A000009, A000041, A168019, A168021, A168121, A168122.

Extensions

Edited by Charles R Greathouse IV, Mar 23 2010

A168121 Triangle T(n,k) read by rows in which column k lists each number A000009 followed by k-1 zeros, for k>0.

Original entry on oeis.org

1, 1, 1, 2, 0, 1, 2, 1, 0, 1, 3, 0, 0, 0, 1, 4, 2, 1, 0, 0, 1, 5, 0, 0, 0, 0, 0, 1, 6, 2, 0, 1, 0, 0, 0, 1, 8, 0, 2, 0, 0, 0, 0, 0, 1, 10, 3, 0, 0, 1, 0, 0, 0, 0, 1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 15, 4, 2, 2, 0, 1, 0, 0, 0, 0, 0, 1
Offset: 1

Views

Author

Omar E. Pol, Dec 02 2009

Keywords

Examples

			Triangle begins:
==================================================
... Column k: 1. 2. 3. 4. 5. 6. 7. 8. 9 10 11 12
. Row ...........................................
...n ............................................
==================================================
.. 1 ........ 1,
.. 2 ........ 1, 1,
.. 3 ........ 2, 0, 1,
.. 4 ........ 2, 1, 0, 1,
.. 5 ........ 3, 0, 0, 0, 1,
.. 6 ........ 4, 2, 1, 0, 0, 1,
.. 7 ........ 5, 0, 0, 0, 0, 0, 1,
.. 8 ........ 6, 2, 0, 1, 0, 0, 0, 1,
.. 9 ........ 8, 0, 2, 0, 0, 0, 0, 0, 1,
. 10 ....... 10, 3, 0, 0, 1, 0, 0, 0, 0, 1,
. 11 ....... 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
. 12 ....... 15, 4, 2, 2, 0, 1, 0, 0, 0, 0, 0, 1,
...

Crossrefs

Cf. A000009, A168021, A168120.

Extensions

Edited by Charles R Greathouse IV, Mar 23 2010

A182720 Triangle read by rows: T(n,k) = A000041(k) if k divides n, T(n,k)=0 otherwise.

Original entry on oeis.org

1, 1, 2, 1, 0, 3, 1, 2, 0, 5, 1, 0, 0, 0, 7, 1, 2, 3, 0, 0, 11, 1, 0, 0, 0, 0, 0, 15, 1, 2, 0, 5, 0, 0, 0, 22, 1, 0, 3, 0, 0, 0, 0, 0, 30, 1, 2, 0, 0, 7, 0, 0, 0, 0, 42, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 1, 2, 3, 5, 0, 11, 0, 0, 0, 0, 0, 77, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 1, 2, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 135, 1, 0, 3, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176
Offset: 1

Views

Author

Omar E. Pol, Nov 28 2010

Keywords

Examples

			1,
1, 2,
1, 0, 3,
1, 2, 0, 5,
1, 0, 0, 0, 7,
1, 2, 3, 0, 0, 11,
1, 0, 0, 0, 0, 0, 15,
1, 2, 0, 5, 0, 0, 0, 22,
1, 0, 3, 0, 0, 0, 0, 0, 30,
1, 2, 0, 0, 7, 0, 0, 0, 0, 42

Crossrefs

Cf. A000005, A000041, A051731, A168016, A168017, A168018, A168021. Positive integers of row n give A168017.
Row sums give A047968.

Programs

  • Maple
    A182720 := proc(n,k) if n mod k = 0 then combinat[numbpart](k); else 0; end if ; end proc:
seq(seq(A182720(n,k),k=1..n),n=1..15) ;

Formula

T(n,k) = A051731(n,k)*A000041(k).
Previous Showing 11-15 of 15 results.

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