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 A336498 Irregular triangle read by rows where T(n,k) is the number of divisors of n! with k prime factors, counted with multiplicity. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row n is row n! of A146291. Row lengths are A022559(n) + 1. LINKS EXAMPLE 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 MATHEMATICA Table[Length[Select[Divisors[n!], PrimeOmega[#]==k&]], {n, 0, 10}, {k, 0, PrimeOmega[n!]}] CROSSREFS A000720 is column k = 1. A008302 is the version for superprimorials. A022559 gives row lengths minus one. A027423 gives row sums. A146291 is the generalization to non-factorials. A336499 is the restriction to divisors in A130091. A000142 lists factorial numbers. A336415 counts uniform divisors of n!. Cf. A000005, A001222, A118914, A124010, A181796, A327526, A336420. Factorial numbers: A002982, A007489, A048656, A054991, A071626, A325272, A325617, A336414, A336415, A336416, A336418. Sequence in context: A110535 A033941 A053256 * A102418 A317989 A106032 Adjacent sequences:  A336495 A336496 A336497 * A336499 A336500 A336501 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Aug 03 2020 STATUS approved

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Last modified August 7 14:54 EDT 2022. Contains 355989 sequences. (Running on oeis4.)