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 1-7 of 7 results.

A341480 Number of ways to write n as an ordered sum of 3 nonprime numbers.

Original entry on oeis.org

1, 0, 0, 3, 0, 3, 3, 3, 9, 4, 9, 12, 12, 15, 21, 19, 27, 30, 30, 39, 42, 46, 54, 60, 61, 75, 72, 91, 90, 108, 99, 129, 123, 142, 147, 168, 156, 201, 180, 217, 213, 246, 235, 279, 255, 304, 297, 336, 327, 375, 342, 412, 390, 447, 423, 492, 453, 529, 507, 573, 538, 630, 579
Offset: 3

Views

Author

Ilya Gutkovskiy, Feb 13 2021

Keywords

Links

Crossrefs

Cf. A005171, A018252, A052284, A076608, A098238, A341408, A341461, A341481, A341482, A341483, A341484, A341485, A341486.

Programs

  • Maple
    b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
    end:
a:= n-> b(n, 3):
seq(a(n), n=3..65);  # Alois P. Heinz, Feb 13 2021
  • Mathematica
    nmax = 65; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^3, {x, 0, nmax}], x] // Drop[#, 3] &

Formula

G.f. g(x)^3 where g(x) is the G.f. of A005171.

A341481 Number of ways to write n as an ordered sum of 4 nonprime numbers.

Original entry on oeis.org

1, 0, 0, 4, 0, 4, 6, 4, 16, 8, 18, 28, 25, 40, 50, 56, 76, 92, 98, 136, 147, 176, 212, 240, 272, 328, 352, 420, 471, 524, 592, 668, 747, 808, 938, 996, 1127, 1232, 1354, 1456, 1658, 1720, 1966, 2052, 2279, 2408, 2700, 2772, 3144, 3232, 3568, 3740, 4117, 4228, 4722
Offset: 4

Views

Author

Ilya Gutkovskiy, Feb 13 2021

Keywords

Links

Crossrefs

Cf. A005171, A018252, A052284, A076608, A340960, A341451, A341462, A341480, A341482, A341483, A341484, A341485, A341486.

Programs

  • Maple
    b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
    end:
a:= n-> b(n, 4):
seq(a(n), n=4..58);  # Alois P. Heinz, Feb 13 2021
  • Mathematica
    nmax = 58; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^4, {x, 0, nmax}], x] // Drop[#, 4] &

Formula

G.f. g(x)^4, where g(x) is the G.f. of A005171.

A341482 Number of ways to write n as an ordered sum of 5 nonprime numbers.

Original entry on oeis.org

1, 0, 0, 5, 0, 5, 10, 5, 25, 15, 30, 55, 45, 85, 105, 126, 180, 220, 260, 360, 415, 510, 650, 745, 915, 1101, 1270, 1525, 1800, 2045, 2440, 2780, 3225, 3660, 4250, 4771, 5465, 6185, 6930, 7840, 8816, 9790, 11015, 12240, 13505, 15146, 16595, 18385, 20240, 22325, 24255
Offset: 5

Views

Author

Ilya Gutkovskiy, Feb 13 2021

Keywords

Crossrefs

Cf. A005171, A018252, A052284, A076608, A340961, A341452, A341464, A341480, A341481, A341483, A341484, A341485, A341486.

Programs

  • Maple
    b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
    end:
a:= n-> b(n, 5):
seq(a(n), n=5..55);  # Alois P. Heinz, Feb 13 2021
  • Mathematica
    nmax = 55; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &

A341483 Number of ways to write n as an ordered sum of 6 nonprime numbers.

Original entry on oeis.org

1, 0, 0, 6, 0, 6, 15, 6, 36, 26, 45, 96, 75, 156, 201, 242, 375, 456, 586, 816, 987, 1256, 1656, 1962, 2512, 3102, 3717, 4616, 5577, 6612, 8067, 9516, 11283, 13372, 15678, 18378, 21412, 24966, 28719, 33388, 38244, 43872, 50248, 57288, 64914, 74074, 83328, 94248
Offset: 6

Views

Author

Ilya Gutkovskiy, Feb 13 2021

Keywords

Crossrefs

Cf. A005171, A018252, A052284, A076608, A340962, A341453, A341465, A341480, A341481, A341482, A341484, A341485, A341486.

Programs

  • Maple
    b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
    end:
a:= n-> b(n, 6):
seq(a(n), n=6..53);  # Alois P. Heinz, Feb 13 2021
  • Mathematica
    nmax = 53; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^6, {x, 0, nmax}], x] // Drop[#, 6] &

A341485 Number of ways to write n as an ordered sum of 8 nonprime numbers.

Original entry on oeis.org

1, 0, 0, 8, 0, 8, 28, 8, 64, 64, 84, 232, 182, 400, 596, 680, 1232, 1520, 2128, 3144, 3970, 5504, 7532, 9584, 12945, 16920, 21464, 28288, 35778, 45264, 57856, 72024, 90036, 112456, 138140, 170600, 208874, 254192, 309088, 373584, 449731, 539408, 645584, 767776
Offset: 8

Views

Author

Ilya Gutkovskiy, Feb 13 2021

Keywords

Crossrefs

Cf. A005171, A018252, A052284, A076608, A340964, A341455, A341467, A341480, A341481, A341482, A341483, A341484, A341486.

Programs

  • Maple
    b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
    end:
a:= n-> b(n, 8):
seq(a(n), n=8..51);  # Alois P. Heinz, Feb 13 2021
  • Mathematica
    nmax = 51; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &

A341486 Number of ways to write n as an ordered sum of 9 nonprime numbers.

Original entry on oeis.org

1, 0, 0, 9, 0, 9, 36, 9, 81, 93, 108, 333, 270, 585, 945, 1047, 2016, 2547, 3612, 5571, 7101, 10227, 14256, 18621, 25830, 34497, 44955, 60610, 78480, 101754, 133092, 169380, 217008, 276852, 347967, 439272, 549786, 683244, 849528, 1047678, 1288017, 1577934
Offset: 9

Views

Author

Ilya Gutkovskiy, Feb 13 2021

Keywords

Crossrefs

Cf. A005171, A018252, A052284, A076608, A340965, A341457, A341468, A341480, A341481, A341482, A341483, A341484, A341485.

Programs

  • Maple
    b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
    end:
a:= n-> b(n, 9):
seq(a(n), n=9..50);  # Alois P. Heinz, Feb 13 2021
  • Mathematica
    nmax = 50; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

A341504 Number of ways to write n as an ordered sum of 10 nonprime numbers.

Original entry on oeis.org

1, 0, 0, 10, 0, 10, 45, 10, 100, 130, 135, 460, 390, 820, 1435, 1552, 3135, 4090, 5805, 9370, 12040, 17890, 25485, 33940, 48385, 65812, 87925, 121040, 160155, 212350, 283666, 368590, 482750, 628390, 806450, 1039382, 1327060, 1682860, 2134730, 2684320, 3364819
Offset: 10

Views

Author

Ilya Gutkovskiy, Feb 13 2021

Keywords

Crossrefs

Cf. A005171, A018252, A052284, A076608, A340966, A341460, A341469, A341480, A341481, A341482, A341483, A341484, A341485, A341486.

Programs

  • Maple
    b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
    end:
a:= n-> b(n, 10):
seq(a(n), n=10..50);  # Alois P. Heinz, Feb 13 2021
  • Mathematica
    nmax = 50; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &
Showing 1-7 of 7 results.

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

Content is available under The OEIS End-User License Agreement.