proposed

approved

editing

proposed

The sorted version is A330972.

A permutation of A330972 (the sorted version)Includes all highly factorable numbers A033833.

Includes all highly factorable numbers (A033833).

Factorizations are A001055, with image A045782, with and complement A330976.

Factorizations of a(n) for n = 1, 4, 8, 12, 16, 24, 36, 60, 48:

Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiplicative_partition">Multiplicative partition</a>

R. E. Canfield, P. Erdős and C. Pomerance, <a href="http://math.dartmouth.edu/~carlp/PDF/paper39.pdf">On a Problem of Oppenheim concerning "Factorisatio Numerorum"</a>, J. Number Theory 17 (1983), 1-28.

From Gus Wiseman, Jan 11 2020: (Start)

Factorizations of a(n) for n = 1, 4, 8, 12, 16, 24, 36, 60, 48:

{} 4 8 12 16 24 36 60 48

2*2 2*4 2*6 2*8 3*8 4*9 2*30 6*8

2*2*2 3*4 4*4 4*6 6*6 3*20 2*24

2*2*3 2*2*4 2*12 2*18 4*15 3*16

2*2*2*2 2*2*6 3*12 5*12 4*12

2*3*4 2*2*9 6*10 2*3*8

2*2*2*3 2*3*6 2*5*6 2*4*6

3*3*4 3*4*5 3*4*4

2*2*3*3 2*2*15 2*2*12

2*3*10 2*2*2*6

2*2*3*5 2*2*3*4

2*2*2*2*3

(End)

All terms belong to A025487.

The strict version is A045780.

A permutation of A330972 (the sorted version).

Includes all highly factorable numbers (A033833).

The least number with exactly n factorizations is A330973(n).

Cf. Factorizations are A001055, with image A045782, with complement A330976.

Strict factorizations are A045778 with image A045779 and complement A330975.

Cf. A070175, A318284, A325238, A330974, A330989, A330992, A330998.

approved

editing

_David W. Wilson (davidwwilson(AT)comcast.net)_

nonn,new

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David W. Wilson (davidwwilson(AT)attbicomcast.comnet)

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David W. Wilson (davidwwilson(AT)attbi.com)

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David Wilson (wilson@ctron.com)

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