A347649 -id:A347649 - cp's OEIS frontend

A347648 Number of partitions of n into at most 2 squarefree parts.

1, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 4, 4, 4, 4, 5, 5, 4, 4, 6, 5, 6, 5, 7, 5, 6, 5, 7, 6, 6, 6, 8, 7, 8, 7, 11, 8, 8, 8, 11, 9, 9, 10, 13, 10, 9, 9, 13, 10, 8, 8, 14, 11, 10, 8, 13, 11, 12, 10, 15, 12, 12, 11, 15, 12, 12, 12, 18, 13, 14, 12, 21, 14, 15, 13

Offset: 0

Ilya Gutkovskiy, Sep 09 2021

nonn

Cf. A005117, A071068, A073576, A347649.

A347655 Number of partitions of n into at most 4 squarefree parts.

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 17, 19, 22, 24, 28, 31, 34, 37, 42, 44, 50, 53, 59, 61, 69, 71, 80, 82, 90, 93, 103, 106, 117, 121, 134, 137, 150, 154, 169, 173, 188, 194, 212, 216, 235, 240, 259, 264, 284, 288, 310, 314, 337, 342, 368, 370, 398, 403, 432

Offset: 0

Ilya Gutkovskiy, Sep 09 2021

nonn

Cf. A005117, A073576, A308767, A347648, A347649, A347656, A347657.

Table[Count[IntegerPartitions[n,4],?(AllTrue[#,SquareFreeQ]&)],{n,0,100}] (* _Harvey P. Dale, Sep 04 2023 *)

A347656 Number of partitions of n into at most 5 squarefree parts.

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 8, 10, 12, 15, 18, 21, 24, 29, 33, 39, 43, 51, 56, 65, 71, 81, 89, 101, 108, 122, 132, 147, 157, 175, 187, 206, 218, 241, 257, 282, 298, 327, 346, 378, 397, 434, 457, 498, 520, 567, 595, 644, 671, 726, 759, 816, 848, 911, 949, 1017, 1053, 1129, 1172

Offset: 0

Ilya Gutkovskiy, Sep 09 2021

nonn

Cf. A005117, A073576, A308840, A347648, A347649, A347655, A347657.

Table[Count[IntegerPartitions[n,5],?(AllTrue[#,SquareFreeQ]&)],{n,0,60}] (* _Harvey P. Dale, Aug 27 2023 *)

A347657 Number of partitions of n into at most 6 squarefree parts.

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 9, 11, 14, 17, 22, 26, 32, 37, 44, 52, 61, 70, 81, 92, 107, 120, 137, 153, 174, 192, 217, 238, 268, 292, 326, 354, 394, 426, 471, 509, 564, 605, 664, 714, 784, 839, 916, 980, 1070, 1141, 1239, 1320, 1435, 1522, 1644, 1745, 1886, 1993, 2143, 2264

Offset: 0

Ilya Gutkovskiy, Sep 09 2021

nonn

Cf. A005117, A073576, A308902, A347648, A347649, A347655, A347656.

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

Ilya Gutkovskiy, Oct 25 2022

nonn

Cf. A005117, A087188, A307835, A347649, A347778, A358023, A358025.

cp's OEIS Frontend

A347648 Number of partitions of n into at most 2 squarefree parts.

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A347655 Number of partitions of n into at most 4 squarefree parts.

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A347656 Number of partitions of n into at most 5 squarefree parts.

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Mathematica

A347657 Number of partitions of n into at most 6 squarefree parts.

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

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Keywords

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