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 1-9 of 9 results.

A341123 Number of partitions of n into 5 prime powers (including 1).

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 9, 11, 15, 17, 23, 25, 32, 34, 42, 45, 55, 56, 68, 71, 83, 84, 100, 100, 117, 118, 136, 135, 158, 153, 179, 178, 204, 200, 234, 226, 261, 255, 291, 283, 327, 310, 357, 344, 390, 371, 430, 405, 466, 444, 505, 476, 550, 511, 589, 557, 634, 589, 684, 629
Offset: 5

Views

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

Crossrefs

Cf. A000961, A010055, A071330, A341112, A341122, A341124, A341125, A341126, A341127.

Programs

  • Maple
    q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
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`(q(i), b(n-i, min(n-i, i), t-1), 0)))
    end:
a:= n-> b(n$2, 5):
seq(a(n), n=5..64);  # Alois P. Heinz, Feb 05 2021
  • Mathematica
    q[n_] := q[n] = Length[FactorInteger[n]] < 2;
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[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
a[n_] := b[n, n, 5];
Table[a[n], {n, 5, 64}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

A341122 Number of partitions of n into 4 prime powers (including 1).

Original entry on oeis.org

1, 1, 2, 3, 5, 5, 8, 9, 12, 13, 17, 17, 22, 22, 26, 27, 33, 31, 39, 38, 44, 43, 51, 47, 58, 54, 63, 60, 71, 64, 79, 74, 88, 82, 99, 88, 108, 97, 116, 105, 126, 110, 134, 119, 141, 126, 153, 133, 164, 143, 172, 149, 184, 155, 194, 168, 204, 173, 215, 180, 227, 192, 238
Offset: 4

Views

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

Crossrefs

Cf. A000961, A010055, A071330, A341112, A341123, A341124, A341125, A341126, A341127.

Programs

  • Maple
    q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
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`(q(i), b(n-i, min(n-i, i), t-1), 0)))
    end:
a:= n-> b(n$2, 4):
seq(a(n), n=4..66);  # Alois P. Heinz, Feb 05 2021
  • Mathematica
    q[n_] := q[n] = Length[FactorInteger[n]] < 2;
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[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
a[n_] := b[n, n, 4];
Table[a[n], {n, 4, 66}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

A341124 Number of partitions of n into 6 prime powers (including 1).

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 10, 12, 17, 20, 27, 31, 41, 45, 56, 63, 77, 83, 101, 108, 128, 136, 160, 168, 196, 204, 236, 245, 281, 288, 331, 340, 387, 395, 450, 457, 519, 525, 594, 598, 677, 678, 763, 764, 855, 851, 957, 949, 1062, 1053, 1177, 1161, 1300, 1276, 1425, 1403, 1564
Offset: 6

Views

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

Crossrefs

Cf. A000961, A010055, A071330, A341112, A341122, A341123, A341125, A341126, A341127.

Programs

  • Maple
    q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
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`(q(i), b(n-i, min(n-i, i), t-1), 0)))
    end:
a:= n-> b(n$2, 6):
seq(a(n), n=6..62);  # Alois P. Heinz, Feb 05 2021
  • Mathematica
    q[n_] := q[n] = Length[FactorInteger[n]] < 2;
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[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
a[n_] := b[n, n, 6];
Table[a[n], {n, 6, 62}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

A341112 Number of partitions of n into 3 prime powers (including 1).

Original entry on oeis.org

1, 1, 2, 3, 4, 4, 6, 6, 8, 8, 10, 9, 12, 10, 13, 12, 15, 13, 17, 15, 18, 15, 19, 16, 21, 17, 23, 18, 24, 19, 27, 23, 30, 24, 32, 25, 32, 26, 34, 26, 36, 26, 36, 28, 38, 28, 40, 30, 42, 32, 43, 30, 45, 32, 47, 35, 49, 30, 50, 35, 51, 36, 53, 35, 55, 37, 54, 40, 57, 36, 61, 40, 61
Offset: 3

Views

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

Crossrefs

Cf. A000961, A010055, A071330, A282064, A307727, A307825, A341122, A341123, A341124, A341125, A341126, A341127.

Programs

  • Maple
    q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
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`(q(i), b(n-i, min(n-i, i), t-1), 0)))
    end:
a:= n-> b(n$2, 3):
seq(a(n), n=3..75);  # Alois P. Heinz, Feb 05 2021
  • Mathematica
    q[n_] := q[n] = Length[FactorInteger[n]] < 2;
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[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
a[n_] := b[n, n, 3];
Table[a[n], {n, 3, 75}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

A341126 Number of partitions of n into 8 prime powers (including 1).

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 10, 13, 19, 23, 32, 38, 51, 60, 77, 90, 113, 128, 158, 179, 215, 240, 287, 316, 373, 409, 475, 517, 599, 645, 741, 799, 908, 971, 1104, 1173, 1326, 1408, 1580, 1670, 1874, 1967, 2198, 2310, 2563, 2680, 2976, 3097, 3426, 3566, 3926, 4070, 4485
Offset: 8

Views

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

Crossrefs

Cf. A000961, A010055, A071330, A341112, A341122, A341123, A341124, A341125, A341127.

Programs

  • Maple
    q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
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`(q(i), b(n-i, min(n-i, i), t-1), 0)))
    end:
a:= n-> b(n$2, 8):
seq(a(n), n=8..60);  # Alois P. Heinz, Feb 05 2021
  • Mathematica
    q[n_] := q[n] = Length[FactorInteger[n]] < 2;
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[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
a[n_] := b[n, n, 8];
Table[a[n], {n, 8, 60}] (* Jean-François Alcover, Feb 22 2022, after _Alois P. Heinz *)

A341127 Number of partitions of n into 9 prime powers (including 1).

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 10, 13, 19, 24, 33, 40, 54, 64, 83, 99, 125, 144, 180, 206, 250, 284, 341, 383, 455, 506, 593, 656, 762, 835, 965, 1054, 1206, 1309, 1491, 1610, 1825, 1964, 2213, 2374, 2664, 2843, 3179, 3387, 3769, 3998, 4440, 4695, 5194, 5480, 6043, 6357
Offset: 9

Views

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

Crossrefs

Cf. A000961, A010055, A071330, A341112, A341122, A341123, A341124, A341125, A341126.

Programs

  • Maple
    q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
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`(q(i), b(n-i, min(n-i, i), t-1), 0)))
    end:
a:= n-> b(n$2, 9):
seq(a(n), n=9..60);  # Alois P. Heinz, Feb 05 2021
  • Mathematica
    q[n_] := q[n] = Length[FactorInteger[n]] < 2;
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[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
a[n_] := b[n, n, 9];
Table[a[n], {n, 9, 60}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

A341144 Number of partitions of n into 7 distinct prime powers (including 1).

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 3, 4, 6, 8, 8, 10, 12, 15, 16, 22, 23, 29, 30, 37, 40, 50, 50, 63, 68, 79, 81, 99, 101, 121, 127, 147, 153, 182, 182, 214, 224, 253, 262, 304, 309, 351, 365, 405, 421, 477, 485, 541, 563, 614, 634, 706, 719, 791, 823, 888, 919, 1006, 1029, 1115, 1164
Offset: 30

Views

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

Crossrefs

Cf. A000961, A010055, A341125, A341132, A341136, A341140, A341141, A341142, A341143, A341145.

Programs

  • Maple
    q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
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`(q(i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 7):
seq(a(n), n=30..90);  # Alois P. Heinz, Feb 05 2021
  • Mathematica
    q[n_] := q[n] = Length[FactorInteger[n]] < 2;
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[q[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
a[n_] := b[n, n, 7];
Table[a[n], {n, 30, 90}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

A341136 Number of ways to write n as an ordered sum of 7 prime powers (including 1).

Original entry on oeis.org

1, 7, 28, 84, 210, 455, 882, 1569, 2611, 4116, 6223, 9093, 12901, 17822, 24053, 31759, 41132, 52367, 65702, 81326, 99526, 120471, 144417, 171493, 201985, 235963, 273889, 315805, 362181, 413021, 468888, 529466, 595770, 667541, 745899, 830473, 922866, 1021832, 1129499
Offset: 7

Views

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

Crossrefs

Cf. A000961, A010055, A282062, A282064, A341125, A341133, A341134, A341135, A341137, A341138, A341139.

Programs

  • Maple
    q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(q(j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n, 7):
seq(a(n), n=7..45);  # Alois P. Heinz, Feb 05 2021
  • Mathematica
    nmax = 45; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &

A341131 Number of partitions of n into 10 prime powers (including 1).

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 10, 13, 19, 24, 34, 41, 56, 67, 87, 105, 134, 156, 196, 228, 278, 320, 387, 439, 526, 593, 698, 783, 915, 1014, 1179, 1304, 1497, 1648, 1884, 2058, 2342, 2551, 2882, 3130, 3524, 3802, 4266, 4595, 5125, 5504, 6124, 6548, 7263, 7750, 8558
Offset: 10

Views

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

Crossrefs

Cf. A000961, A010055, A071330, A341112, A341122, A341123, A341124, A341125, A341126, A341127.

Programs

  • Maple
    q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
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`(q(i), b(n-i, min(n-i, i), t-1), 0)))
    end:
a:= n-> b(n$2, 10):
seq(a(n), n=10..60);  # Alois P. Heinz, Feb 05 2021
  • Mathematica
    q[n_] := q[n] = Length[FactorInteger[n]] < 2;
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[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
a[n_] := b[n, n, 10];
Table[a[n], {n, 10, 60}] (* Jean-François Alcover, Feb 27 2022, after Alois P. Heinz *)
Showing 1-9 of 9 results.

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