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.

A341073 Number of partitions of n into 4 distinct squarefree parts.

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 3, 2, 5, 7, 8, 7, 11, 13, 15, 13, 17, 20, 23, 21, 28, 33, 34, 32, 40, 44, 47, 44, 55, 63, 66, 62, 75, 84, 87, 81, 98, 110, 115, 109, 127, 144, 148, 140, 159, 180, 186, 177, 199, 220, 231, 217, 241, 264, 275, 262, 290, 317, 325, 314, 343, 376, 382, 368, 403
Offset: 11

Views

Author

Ilya Gutkovskiy, Feb 04 2021

Keywords

Links

Crossrefs

Cf. A005117, A008966, A098236, A307835, A308767, A341064, A341074, A341075, A341095, A341096, A341097, A341098.

Programs

  • Maple
    b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 4):
seq(a(n), n=11..75);  # Alois P. Heinz, Feb 04 2021
  • Mathematica
    b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
     If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
a[n_] := b[n, n, 4];
Table[a[n], {n, 11, 75}] (* Jean-François Alcover, Jul 14 2021, after Alois P. Heinz *)

A341074 Number of partitions of n into 5 distinct squarefree parts.

Original entry on oeis.org

1, 1, 1, 0, 2, 3, 3, 3, 5, 8, 9, 8, 11, 15, 16, 16, 22, 27, 30, 31, 38, 46, 48, 49, 57, 72, 73, 76, 90, 107, 109, 112, 128, 151, 156, 160, 182, 214, 220, 224, 250, 290, 297, 306, 335, 387, 399, 409, 442, 503, 517, 529, 572, 641, 660, 676, 726, 809, 829, 846, 903
Offset: 17

Views

Author

Ilya Gutkovskiy, Feb 04 2021

Keywords

Crossrefs

Cf. A005117, A008966, A098236, A307835, A308840, A341065, A341073, A341075, A341095, A341096, A341097, A341098.

Programs

  • Maple
    b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 5):
seq(a(n), n=17..77);  # Alois P. Heinz, Feb 04 2021
  • Mathematica
    b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
     If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
a[n_] := b[n, n, 5];
Table[a[n], {n, 17, 77}] (* Jean-François Alcover, Jul 14 2021, after Alois P. Heinz *)
Table[Count[IntegerPartitions[n,{5}],?(Length[Union[#]]==5&&AllTrue[#,SquareFreeQ]&)],{n,17,80}] (* _Harvey P. Dale, Sep 05 2023 *)

A341075 Number of partitions of n into 6 distinct squarefree parts.

Original entry on oeis.org

1, 0, 0, 1, 2, 2, 2, 3, 6, 5, 6, 7, 12, 12, 15, 18, 26, 26, 28, 34, 44, 46, 50, 60, 77, 79, 86, 98, 122, 126, 134, 154, 188, 196, 207, 236, 277, 292, 305, 343, 400, 423, 443, 492, 567, 596, 624, 686, 779, 819, 856, 938, 1052, 1108, 1149, 1255, 1394, 1463, 1515, 1646, 1818
Offset: 24

Views

Author

Ilya Gutkovskiy, Feb 04 2021

Keywords

Crossrefs

Cf. A005117, A008966, A098236, A307835, A308902, A341066, A341073, A341074, A341095, A341096, A341097, A341098.

Programs

  • Maple
    b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 6):
seq(a(n), n=24..84);  # Alois P. Heinz, Feb 04 2021
  • Mathematica
    Table[Length[Select[IntegerPartitions[n,{6}],Length[Union[#]]==6&&AllTrue[ #,SquareFreeQ]&]],{n,24,90}] (* Harvey P. Dale, Jan 16 2022 *)

A341095 Number of partitions of n into 7 distinct squarefree parts.

Original entry on oeis.org

1, 1, 0, 1, 2, 2, 2, 4, 6, 7, 7, 10, 14, 15, 15, 21, 28, 32, 32, 44, 53, 60, 60, 76, 93, 103, 107, 131, 157, 172, 178, 211, 247, 273, 283, 333, 384, 423, 439, 507, 577, 629, 657, 747, 846, 917, 960, 1078, 1211, 1306, 1362, 1521, 1691, 1822, 1898, 2103, 2322, 2494, 2596, 2850, 3134
Offset: 34

Views

Author

Ilya Gutkovskiy, Feb 04 2021

Keywords

Crossrefs

Cf. A005117, A008966, A098236, A307835, A308952, A341067, A341073, A341074, A341075, A341096, A341097, A341098.

Programs

  • Maple
    b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 7):
seq(a(n), n=34..94);  # Alois P. Heinz, Feb 04 2021
  • Mathematica
    b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
     If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
a[n_] := b[n, n, 7];
Table[a[n], {n, 34, 94}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)

A341096 Number of partitions of n into 8 distinct squarefree parts.

Original entry on oeis.org

1, 0, 1, 2, 2, 1, 3, 4, 5, 5, 8, 12, 14, 13, 18, 24, 28, 27, 38, 49, 55, 57, 71, 89, 99, 104, 125, 156, 171, 183, 217, 259, 285, 303, 353, 416, 457, 486, 559, 653, 710, 758, 858, 992, 1073, 1148, 1284, 1468, 1591, 1693, 1881, 2128, 2296, 2438, 2694, 3018, 3251, 3455, 3783, 4218, 4522
Offset: 45

Views

Author

Ilya Gutkovskiy, Feb 04 2021

Keywords

Crossrefs

Cf. A005117, A008966, A098236, A307835, A326443, A341068, A341073, A341074, A341075, A341095, A341097, A341098.

Programs

  • Maple
    b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 8):
seq(a(n), n=45..105);  # Alois P. Heinz, Feb 04 2021
  • Mathematica
    b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
     If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
a[n_] := b[n, n, 8];
Table[a[n], {n, 45, 105}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)

A341097 Number of partitions of n into 9 distinct squarefree parts.

Original entry on oeis.org

1, 1, 1, 1, 3, 2, 3, 3, 7, 7, 8, 10, 16, 18, 18, 22, 33, 35, 39, 47, 65, 69, 77, 89, 117, 126, 138, 163, 205, 223, 242, 282, 344, 376, 407, 466, 561, 612, 664, 751, 889, 966, 1047, 1176, 1365, 1488, 1606, 1792, 2056, 2240, 2406, 2672, 3032, 3286, 3532, 3891
Offset: 58

Views

Author

Ilya Gutkovskiy, Feb 04 2021

Keywords

Crossrefs

Cf. A005117, A008966, A098236, A307835, A326522, A341069, A341073, A341074, A341075, A341095, A341096, A341098.

Programs

  • Maple
    b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 9):
seq(a(n), n=58..113);  # Alois P. Heinz, Feb 04 2021
  • Mathematica
    b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
     If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
a[n_] := b[n, n, 9];
Table[a[n], {n, 58, 113}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)

A341098 Number of partitions of n into 10 distinct squarefree parts.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 2, 4, 6, 8, 7, 10, 14, 17, 17, 22, 32, 35, 37, 47, 62, 71, 72, 91, 114, 132, 136, 167, 205, 234, 247, 293, 355, 398, 426, 497, 590, 661, 708, 819, 956, 1066, 1141, 1306, 1501, 1672, 1791, 2030, 2318, 2559, 2747, 3081, 3490, 3835, 4115
Offset: 72

Views

Author

Ilya Gutkovskiy, Feb 04 2021

Keywords

Crossrefs

Cf. A005117, A008966, A098236, A307835, A326626, A341070, A341073, A341074, A341075, A341095, A341096, A341097.

Programs

  • Maple
    b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 10):
seq(a(n), n=72..126);  # Alois P. Heinz, Feb 04 2021
  • Mathematica
    b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
     If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
a[n_] := b[n, n, 10];
Table[a[n], {n, 72, 126}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)

A358024 Number of partitions of n into at most 3 distinct squarefree parts.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 3, 3, 4, 4, 5, 5, 5, 7, 8, 8, 9, 10, 13, 12, 13, 14, 17, 16, 18, 17, 21, 20, 21, 23, 26, 25, 26, 27, 32, 31, 33, 36, 40, 40, 39, 42, 48, 47, 47, 50, 58, 56, 55, 58, 66, 64, 61, 67, 75, 74, 70, 74, 84, 83, 79, 82, 93, 91, 89, 93, 103, 102, 97, 105, 115
Offset: 0

Views

Author

Ilya Gutkovskiy, Oct 25 2022

Keywords

Crossrefs

Cf. A005117, A087188, A307835, A347649, A347778, A358023, A358025.
Showing 1-8 of 8 results.

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