A347655 -id:A347655 - cp's OEIS frontend

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

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.

A358025 Number of partitions of n into at most 4 distinct squarefree parts.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 3, 3, 4, 4, 5, 6, 6, 8, 9, 10, 13, 13, 15, 17, 20, 22, 24, 27, 31, 32, 34, 37, 41, 46, 47, 53, 59, 61, 64, 71, 77, 83, 84, 95, 102, 108, 110, 122, 131, 137, 139, 154, 165, 173, 175, 191, 205, 215, 215, 233, 250, 260, 261, 282, 299, 313, 310, 332, 353, 368

Offset: 0

Ilya Gutkovskiy, Oct 25 2022

nonn

Cf. A005117, A087188, A341073, A347586, A347655, A347779, A358023, A358024.

cp's OEIS Frontend

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

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

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A358025 Number of partitions of n into at most 4 distinct squarefree parts.

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