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 1-8 of 8 results.

A216258 Numbers n such that 4n is a partition number.

Original entry on oeis.org

14, 44, 198, 609, 1401, 112819, 178805, 207955, 325039, 580880, 1021992, 1772375, 2029566, 3033041, 3949119, 6635915, 23167430, 29528576, 37549534, 47642323, 96069084, 120875711, 135486560, 190250539, 212844157, 297227062, 331927519, 461087390, 572830228
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Examples

			14 is in the sequence because 4*14 = 56 and 56 is a partition number: p(11) = A000041(11) = 56.

Crossrefs

Cf. A000041, A213179, A213365, A217725, A217726, A222175, A222178, A222179, A225317, A225323, A225324.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 4] == 0 &]/4 (* T. D. Noe, May 05 2013 *)

Formula

a(j) = A225324(j)/4.

Extensions

a(9)-a(29) from R. J. Mathar, May 05 2013

A225325 Partition numbers of the form 5k.

Original entry on oeis.org

5, 15, 30, 135, 385, 490, 1255, 1575, 3010, 4565, 12310, 26015, 31185, 75175, 173525, 386155, 715220, 831820, 1121505, 1741630, 2323520, 3087735, 3554345, 4697205, 7089500, 13848650, 20506255, 26543660, 49995925, 92669720, 133230930, 169229875
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008587 and A000041.

Examples

			15 is in the sequence because 5*3 = 15 and 15 is a partition number: p(7) = A000041(7) = 15.

Links

Crossrefs

Cf. A000041, A008587, A052001, A072871, A087183, A225324, A225326, A225327, A225358, A225360, A127544, A225361

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 5] == 0 &] (* T. D. Noe, May 05 2013 *)
  • PARI
    for(n=9, 1e3, t=numbpart(n); if(t%5, , print1(t", "))) \\ Charles R Greathouse IV, May 08 2013

Formula

a(n) = 5*A217725(n). - Omar E. Pol, May 08 2013

A225326 Partition numbers of the form 6k.

Original entry on oeis.org

30, 42, 792, 1002, 2436, 5604, 37338, 105558, 614154, 4087968, 8118264, 15796476, 133230930, 384276336, 2841940500, 3163127352, 4835271870, 7346629512, 18440293320, 30388671978, 45060624582, 107438159466, 142798995930, 684957390936, 1820701100652
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008588 and A000041.

Examples

			30 is in the sequence because 6*5 = 30 and 30 is a partition number: p(9) = A000041(9) = 30.

Links

Crossrefs

Cf. A000041, A008588, A052001, A072871, A087183, A225324, A225325, A225327, A225358, A225360, A127544, A225361

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 6] == 0 &] (* T. D. Noe, May 05 2013 *)
  • PARI
    for(n=9,1e3,t=numbpart(n);if(t%6,,print1(t", "))) \\ Charles R Greathouse IV, May 08 2013

Formula

a(n) = 6*A217726(n). - Omar E. Pol, May 08 2013

Extensions

a(8)-a(25) from T. D. Noe, May 05 2013

A225327 Partition numbers of the form 7k.

Original entry on oeis.org

7, 42, 56, 77, 231, 385, 490, 1575, 2436, 3010, 10143, 21637, 31185, 37338, 44583, 124754, 147273, 281589, 329931, 386155, 451276, 1121505, 3087735, 8118264, 9289091, 20506255, 23338469, 49995925, 118114304, 133230930, 271248950, 607163746
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008589 and A000041.

Examples

			42 is in the sequence because 7*6 = 42 and 42 is a partition number: p(10) = A000041(10) = 42.

Links

Crossrefs

Cf. A000041, A008589, A052001, A072871, A087183, A225324, A225325, A225326, A225358, A225360, A127544, A225361.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 7] == 0 &]

Formula

a(n) = 7*A222175(n).

A225358 Partition numbers of the form 8k.

Original entry on oeis.org

56, 176, 792, 2323520, 4087968, 8118264, 92669720, 118114304, 150198136, 384276336, 541946240, 1188908248, 1844349560, 2291320912, 3163127352, 4351078600, 5371315400, 5964539504, 7346629512, 10015581680, 11097645016, 16670689208, 18440293320
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008590 and A000041.

Examples

			56 is in the sequence because 8*7 = 56 and 56 is a partition number: p(11) = A000041(11) = 56.

Links

Crossrefs

Cf. A000041, A008590, A052001, A072871, A087183, A225324, A225325, A225326, A225327, A225360, A127544, A225361.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 8] == 0 &]

Formula

a(n) = 8*A222178(n).

A225360 Partition numbers of the form 9k.

Original entry on oeis.org

135, 297, 792, 1575, 10143, 31185, 63261, 329931, 15796476, 44108109, 4835271870, 7346629512, 12292341831, 18440293320, 107438159466, 129913904637, 156919475295, 250438925115, 1527273599625, 3345365983698, 3646072432125, 7206841706490
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008591 and A000041.

Examples

			135 is in the sequence because 9*15 = 135 and 135 is a partition number: p(14) = A000041(14) = 135.

Links

Crossrefs

Cf. A000041, A008591, A052001, A072871, A087183, A225324, A225325, A225326, A225327, A225358, A127544, A225361.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 9] == 0 &]

Formula

a(n) = 9*A222179(n).

A225361 Partition numbers of the form 11k.

Original entry on oeis.org

11, 22, 77, 176, 231, 297, 385, 627, 792, 1958, 3718, 4565, 6842, 8349, 14883, 21637, 26015, 31185, 44583, 53174, 63261, 173525, 204226, 239943, 281589, 386155, 526823, 715220, 831820, 1121505, 1300156, 1741630, 5392783, 7089500, 8118264, 12132164, 18004327
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Intersection of A008593 and A000041.

Examples

			22 is in the sequence because 11*2 = 22 and 22 is a partition number: p(8) = A000041(8) = 22.

Crossrefs

Cf. A000041, A008593, A052001, A072871, A087183, A225324, A225325, A225326, A225327, A225358, A225360, A127544.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 11] == 0 &]

Formula

a(n) = 11*A225323(n).

A278196 Partition numbers (A000041) of the form 2^2 * k for odd k.

Original entry on oeis.org

2436, 5604, 451276, 715220, 831820, 1300156, 7089500, 12132164, 15796476, 26543660, 190569292, 483502844, 761002156, 851376628, 1327710076, 2841940500, 3519222692, 9035836076, 54770336324, 1280011042268, 1820701100652, 3972999029388, 6085253859260
Offset: 1

Views

Author

Colin Barker, Nov 15 2016

Keywords

Comments

Also partition numbers having twice as many even divisors as odd divisors.
A subsequence of A225324.

Links

Crossrefs

Cf. A275029, A278197, A278198, A278199, A278200, A278201.

Programs

  • Mathematica
    Select[PartitionsP@ Range@ 210, Count[#, k_ /; EvenQ@ k] == 2 Count[#, k_ /; OddQ@ k] &@ Divisors@ # &] (* Michael De Vlieger, Nov 15 2016 *)
  • PARI
    maxk=300; L=List(); for(k=1, maxk, p=numbpart(k); if(p%2^2==0 & p\2^2%2==1, listput(L, p))); Vec(L)
Showing 1-8 of 8 results.

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