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.

A341914 Number of partitions of n into 10 distinct and relatively prime parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 97, 128, 164, 212, 267, 340, 423, 530, 653, 807, 984, 1204, 1455, 1761, 2112, 2534, 3015, 3590, 4242, 5013, 5888, 6912, 8070, 9418, 10936, 12690, 14663, 16928, 19466, 22367, 25608, 29292, 33401, 38047, 43214, 49037, 55494, 62740, 70760, 79725, 89623
Offset: 55

Views

Author

Ilya Gutkovskiy, Feb 23 2021

Keywords

Links

Crossrefs

Cf. A023022, A023030, A023035, A078374, A101271, A339672, A340719, A341868, A341870, A341912, A341913.

Programs

  • Mathematica
    nmax = 108; CoefficientList[Series[Sum[MoebiusMu[k] x^(55 k)/Product[1 - x^(j k), {j, 1, 10}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 55] &

Formula

G.f.: Sum_{k>=1} mu(k)* x^(55*k) / Product_{j=1..10} (1 - x^(j*k)).
a(n) <= A008639(n-55), equality for n<110. - R. J. Mathar, Feb 28 2021

A339672 Number of partitions of n into 7 distinct and relatively prime parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 15, 21, 28, 38, 49, 65, 82, 105, 131, 164, 201, 248, 300, 364, 436, 522, 618, 733, 860, 1009, 1175, 1366, 1579, 1823, 2093, 2398, 2738, 3117, 3539, 4006, 4526, 5095, 5731, 6419, 7190, 8018, 8946, 9932, 11044, 12213, 13534, 14912, 16475, 18089, 19928, 21808
Offset: 28

Views

Author

Ilya Gutkovskiy, Feb 23 2021

Keywords

Crossrefs

Cf. A023022, A023027, A023032, A078374, A101271, A340719, A341868, A341870, A341912, A341913, A341914.

Programs

  • Mathematica
    nmax = 80; CoefficientList[Series[Sum[MoebiusMu[k] x^(28 k)/Product[1 - x^(j k), {j, 1, 7}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 28] &

Formula

G.f.: Sum_{k>=1} mu(k)* x^(28*k) / Product_{j=1..7} (1 - x^(j*k)).

A341868 Number of partitions of n into 4 distinct and relatively prime parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 9, 11, 15, 18, 22, 27, 33, 39, 45, 54, 61, 72, 79, 94, 101, 120, 127, 149, 158, 185, 189, 225, 231, 267, 274, 321, 319, 378, 377, 435, 439, 511, 495, 588, 577, 661, 656, 764, 729, 863, 836, 954, 939, 1089, 1022, 1215, 1165, 1323, 1289, 1492, 1392, 1650, 1566, 1776, 1715
Offset: 10

Views

Author

Ilya Gutkovskiy, Feb 23 2021

Keywords

Crossrefs

Cf. A000742, A023022, A023024, A078374, A101271, A339672, A340719, A341870, A341912, A341913, A341914.

Programs

  • Mathematica
    nmax = 70; CoefficientList[Series[Sum[MoebiusMu[k] x^(10 k)/Product[1 - x^(j k), {j, 1, 4}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 10] &

Formula

G.f.: Sum_{k>=1} mu(k)* x^(10*k) / Product_{j=1..4} (1 - x^(j*k)).

A341870 Number of partitions of n into 6 distinct and relatively prime parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 58, 71, 90, 110, 136, 163, 199, 235, 282, 330, 391, 453, 532, 610, 709, 808, 931, 1052, 1206, 1353, 1540, 1718, 1945, 2158, 2432, 2682, 3009, 3305, 3692, 4035, 4493, 4891, 5427, 5883, 6510, 7033, 7758, 8352, 9192, 9862, 10829, 11584, 12687, 13539
Offset: 21

Views

Author

Ilya Gutkovskiy, Feb 23 2021

Keywords

Crossrefs

Cf. A023022, A023026, A023031, A078374, A101271, A339672, A340719, A341868, A341912, A341913, A341914.

Programs

  • Mathematica
    nmax = 76; CoefficientList[Series[Sum[MoebiusMu[k] x^(21 k)/Product[1 - x^(j k), {j, 1, 6}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 21] &

Formula

G.f.: Sum_{k>=1} mu(k)* x^(21*k) / Product_{j=1..6} (1 - x^(j*k)).

A341912 Number of partitions of n into 5 distinct and relatively prime parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70, 83, 101, 118, 141, 162, 192, 218, 255, 286, 333, 370, 427, 470, 540, 590, 673, 730, 831, 894, 1014, 1085, 1224, 1305, 1469, 1552, 1747, 1841, 2057, 2163, 2418, 2520, 2818, 2933, 3256, 3388, 3765, 3879, 4319, 4452, 4914, 5068
Offset: 15

Views

Author

Ilya Gutkovskiy, Feb 23 2021

Keywords

Crossrefs

Cf. A000743, A023022, A023025, A078374, A101271, A339672, A340719, A341868, A341870, A341913, A341914.

Programs

  • Mathematica
    nmax = 70; CoefficientList[Series[Sum[MoebiusMu[k] x^(15 k)/Product[1 - x^(j k), {j, 1, 5}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 15] &

Formula

G.f.: Sum_{k>=1} mu(k)* x^(15*k) / Product_{j=1..5} (1 - x^(j*k)).
a(n) <= A001401(n-15). - R. J. Mathar, Feb 28 2021

A341913 Number of partitions of n into 9 distinct and relatively prime parts.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 54, 73, 94, 123, 157, 201, 252, 318, 393, 488, 598, 732, 887, 1076, 1291, 1549, 1845, 2194, 2592, 3060, 3589, 4206, 4904, 5708, 6615, 7657, 8824, 10156, 11648, 13338, 15224, 17354, 19720, 22380, 25330, 28629, 32277, 36347, 40829, 45812, 51291, 57358
Offset: 45

Views

Author

Ilya Gutkovskiy, Feb 23 2021

Keywords

Crossrefs

Cf. A023022, A023029, A023034, A078374, A101271, A339672, A340719, A341868, A341870, A341912, A341914.

Programs

  • Mathematica
    nmax = 97; CoefficientList[Series[Sum[MoebiusMu[k] x^(45 k)/Product[1 - x^(j k), {j, 1, 9}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 45] &

Formula

G.f.: Sum_{k>=1} mu(k)* x^(45*k) / Product_{j=1..9} (1 - x^(j*k)).
Showing 1-6 of 6 results.

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