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 1-2 of 2 results.

A307835 Number of partitions of n into 3 distinct squarefree parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 2, 2, 3, 5, 4, 4, 5, 9, 8, 8, 9, 12, 11, 11, 12, 16, 15, 15, 17, 21, 19, 18, 20, 25, 24, 22, 28, 33, 32, 28, 33, 40, 37, 35, 40, 50, 47, 42, 48, 58, 56, 48, 56, 65, 66, 57, 63, 73, 73, 65, 70, 82, 80, 74, 81, 92, 90, 80, 92, 102, 102, 88, 104, 116, 116
Offset: 0

Views

Author

Ilya Gutkovskiy, May 01 2019

Keywords

Examples

			a(15) = 4 because we have [11, 3, 1], [10, 3, 2], [7, 6, 2] and [7, 5, 3].
		

Crossrefs

Programs

  • Mathematica
    Table[Count[IntegerPartitions[n, {3}], _?(And[UnsameQ @@ #, AllTrue[#, SquareFreeQ[#] &]] &)], {n, 0, 75}]

Formula

a(n) = [x^n y^3] Product_{k>=1} (1 + mu(k)^2*y*x^k).

A347649 Number of partitions of n into at most 3 squarefree parts.

Original entry on oeis.org

1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 9, 11, 11, 13, 13, 16, 15, 17, 17, 20, 20, 23, 22, 25, 25, 28, 27, 30, 30, 33, 32, 37, 37, 41, 41, 45, 44, 50, 47, 54, 53, 60, 57, 64, 63, 68, 65, 72, 71, 76, 71, 80, 80, 86, 78, 89, 90, 98, 89, 98, 99, 109, 99, 110
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 09 2021

Keywords

Crossrefs

Showing 1-2 of 2 results.