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A336498
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Irregular triangle read by rows where T(n,k) is the number of divisors of n! with k prime factors, counted with multiplicity.
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6
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1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 4, 4, 3, 1, 1, 3, 5, 6, 6, 5, 3, 1, 1, 4, 8, 11, 12, 11, 8, 4, 1, 1, 4, 8, 11, 12, 12, 12, 12, 11, 8, 4, 1, 1, 4, 8, 12, 16, 19, 20, 20, 19, 16, 12, 8, 4, 1, 1, 4, 9, 15, 21, 26, 29, 30, 30, 29, 26, 21, 15, 9, 4, 1
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OFFSET
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0,6
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COMMENTS
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LINKS
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EXAMPLE
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Triangle begins:
1
1
1 1
1 2 1
1 2 2 2 1
1 3 4 4 3 1
1 3 5 6 6 5 3 1
1 4 8 11 12 11 8 4 1
1 4 8 11 12 12 12 12 11 8 4 1
1 4 8 12 16 19 20 20 19 16 12 8 4 1
Row n = 6 counts the following divisors:
1 2 4 8 16 48 144 720
3 6 12 24 72 240
5 9 18 36 80 360
10 20 40 120
15 30 60 180
45 90
Row n = 7 counts the following divisors:
1 2 4 8 16 48 144 720 5040
3 6 12 24 72 240 1008
5 9 18 36 80 336 1680
7 10 20 40 112 360 2520
14 28 56 120 504
15 30 60 168 560
21 42 84 180 840
35 45 90 252 1260
63 126 280
70 140 420
105 210 630
315
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MATHEMATICA
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Table[Length[Select[Divisors[n!], PrimeOmega[#]==k&]], {n, 0, 10}, {k, 0, PrimeOmega[n!]}]
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CROSSREFS
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A008302 is the version for superprimorials.
A022559 gives row lengths minus one.
A146291 is the generalization to non-factorials.
A336415 counts uniform divisors of n!.
Factorial numbers: A002982, A007489, A048656, A054991, A071626, A325272, A325617, A336414, A336415, A336416, A336418.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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