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 1-6 of 6 results.

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)

A278197 Partition numbers (A000041) of the form 2^3 * k for odd k.

Original entry on oeis.org

56, 792, 8118264, 92669720, 150198136, 1188908248, 1844349560, 3163127352, 4351078600, 5371315400, 7346629512, 11097645016, 16670689208, 18440293320, 684957390936, 6622987708040, 51820051838712, 77195892663512, 133978259344888, 197726516681672
Offset: 1

Views

Author

Colin Barker, Nov 15 2016

Keywords

Comments

Also partition numbers having three times as many even divisors as odd divisors.

Links

Crossrefs

Cf. A275029, A278196, A278198, A278199, A278200, A278201.

Programs

  • Mathematica
    Select[PartitionsP@ Range@ 250, Count[#, k_ /; EvenQ@ k] == 3 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%2^3==0 & p\2^3%2==1, listput(L, p))); Vec(L)

A278199 Partition numbers (A000041) of the form 2^5 * k for odd k.

Original entry on oeis.org

4087968, 625846753120, 576672674947168, 1896564103591584, 21424521360255636320, 61382395164161775318496, 25744258930034131533263392, 54951205445179608281719072, 1317709210896221493178043552, 172557592110602218633091543840, 6647848746214407376439536432805536
Offset: 1

Views

Author

Colin Barker, Nov 15 2016

Keywords

Comments

Also partition numbers having five times as many even divisors as odd divisors.

Links

Crossrefs

Cf. A275029, A278196, A278197, A278198, A278200, A278201.

Programs

  • Mathematica
    Select[PartitionsP@ Range@ 1200, Count[#, k_ /; EvenQ@ k] == 5 Count[#, k_ /; OddQ@ k] &@ Divisors@ # &] (* Michael De Vlieger, Nov 15 2016 *)
  • PARI
    maxk=1400; L=List(); for(k=1, maxk, p=numbpart(k); if(p%2^5==0 & p\2^5%2==1, listput(L, p))); Vec(L)

A278200 Partition numbers (A000041) of the form 2^6 * k for odd k.

Original entry on oeis.org

2323520, 37027355200, 8030248384943040, 55733465144636286656, 134508188001572923840, 6179690078238084808000, 975509982873756796925504, 69523232218023552371152320, 638864582333908382360557376, 1151097146124113726578727360, 1204186073016375022219516992
Offset: 1

Views

Author

Colin Barker, Nov 15 2016

Keywords

Comments

Also partition numbers having six times as many even divisors as odd divisors.

Links

Crossrefs

Cf. A275029, A278196, A278197, A278198, A278199, A278201.

Programs

  • Mathematica
    Select[PartitionsP@ Range@ 1500, Count[#, k_ /; EvenQ@ k] == 6 Count[#, k_ /; OddQ@ k] &@ Divisors@ # &] (* Michael De Vlieger, Nov 15 2016 *)
  • PARI
    maxk=1000; L=List(); for(k=1, maxk, p=numbpart(k); if(p%2^6==0 & p\2^6%2==1, listput(L, p))); Vec(L)

A278201 Partition numbers (A000041) of the form 2^7 * k for odd k.

Original entry on oeis.org

541946240, 47826239745920, 49760750604354432757376, 18426207875324210441995136, 914345304752746677204951178080640, 377394877138559089794329589034333523822720, 33381228189530831120385246576357623531476650368, 23951815370456759593096244705083096637451017834880
Offset: 1

Views

Author

Colin Barker, Nov 15 2016

Keywords

Comments

Also partition numbers having seven times as many even divisors as odd divisors.

Links

Crossrefs

Cf. A275029, A278196, A278197, A278198, A278199, A278200.

Programs

  • Mathematica
    Select[PartitionsP@ Range@ 2000, Count[#, k_ /; EvenQ@ k] == 7 Count[#, k_ /; OddQ@ k] &@ Divisors@ # &] (* Michael De Vlieger, Nov 15 2016 *)
  • PARI
    maxk=3000; L=List(); for(k=1, maxk, p=numbpart(k); if(p%2^7==0 & p\2^7%2==1, listput(L, p))); Vec(L)

A278781 Numbers m such that A000041(m) is of the form 2^4 * k for odd k.

Original entry on oeis.org

15, 106, 122, 131, 136, 253, 295, 327, 339, 383, 412, 449, 465, 517, 520, 551, 580, 581, 599, 602, 632, 648, 669, 677, 776, 806, 815, 838, 904, 927, 1071, 1137, 1166, 1174, 1199, 1263, 1275, 1298, 1325, 1375, 1399, 1404, 1425, 1554, 1564, 1641, 1684, 1688
Offset: 1

Views

Author

Colin Barker, Nov 28 2016

Keywords

Comments

Numbers m such that A278478(m) = 4.
Also numbers m such that A000041(m) has four times as many even divisors as odd divisors.

Links

Crossrefs

Cf. A000041, A278198, A278779, A278780, A278782, A278783, A278784.
Positions of 4's in A278478.

Programs

  • Mathematica
    Select[Range[1700], IntegerExponent[PartitionsP[#], 2] == 4 &] (* Amiram Eldar, May 25 2024 *)
  • PARI
    isok(n) = valuation(numbpart(n), 2)==4;
select(n->isok(n), vector(2000, n, n))

Formula

A000041(a(n)) = A278198(n).
Showing 1-6 of 6 results.

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