The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A256384 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A256384

Number A(n,k) of factorizations of m^n into at most n factors, where m is a product of exactly k distinct primes; square array A(n,k), n>=0, k>=0, read by antidiagonals.
(history; published version)

#19 by Alois P. Heinz at Fri Oct 26 16:15:09 EDT 2018

STATUS

editing

approved

#18 by Alois P. Heinz at Wed Oct 24 15:32:16 EDT 2018

EXAMPLE

1, 1, 1, 1, 1, 1, ...

1, 2, 5, 14, 41, 122, ...

1, 3, 19, 171, 1675, 16683, ...

1, 5, 74, 1975, 64182, 2203215, ...

1, 7, 248, 20096, 2213016, 268446852, ...

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approved

editing

#17 by Bruno Berselli at Fri Jan 08 05:28:39 EST 2016

STATUS

proposed

approved

#16 by Jean-François Alcover at Fri Jan 08 05:22:57 EST 2016

STATUS

editing

proposed

#15 by Jean-François Alcover at Fri Jan 08 05:22:48 EST 2016

MATHEMATICA

b[n_, k_, i_] := b[n, k, i] = If[n>k, 0, 1] + If[PrimeQ[n] || i<2, 0, Sum[ If[d > k, 0, b[n/d, d, i-1]], {d, Divisors[n][[2 ;; -2]]}]]; A[0, _] = 1; A[1, _] = 1; A[_, 0] = 1; A[n_, k_] := With[{t = Times @@ Prime[ Range[k] ]}, b[t^n, t^n, n]]; Table[diag = Table[A[n-k, k], {k, n, 0, -1}]; Print[ diag]; diag, {n, 0, 10}] // Flatten (* Jean-François Alcover, Jan 08 2016, after Alois P. Heinz *)

STATUS

approved

editing

#14 by Alois P. Heinz at Tue Mar 31 20:25:45 EDT 2015

STATUS

editing

approved

#13 by Alois P. Heinz at Tue Mar 31 20:25:35 EDT 2015

EXAMPLE

A(2,2) = 5: (2*3)^2 = 36 has 9 5 factorizations into at most 2 factors: 36, 2*18, 3*12, 4*9, 6*6.

#12 by Alois P. Heinz at Mon Mar 30 19:41:03 EDT 2015

CROSSREFS

Rows n=0+1,2 -3 give: A000012, A007051, A256493.

STATUS

approved

editing

#11 by Alois P. Heinz at Sun Mar 29 16:44:49 EDT 2015

STATUS

editing

approved

#10 by Alois P. Heinz at Fri Mar 27 21:22:42 EDT 2015

EXAMPLE

A(2,2) = 5: (2*3)^2 = 36 has 9 factorizations into at most 2 factors: 36, 2*18, 3*12, 4*9, 6*6.