A277239 Number A(n,k) of factorizations of m^n into exactly k factors, where m is a product of two distinct primes; square array A(n,k), n>=0, k>=0, read by antidiagonals.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 5, 1, 0, 1, 2, 8, 8, 1, 0, 1, 2, 9, 19, 13, 1, 0, 1, 2, 9, 27, 42, 18, 1, 0, 1, 2, 9, 30, 74, 78, 25, 1, 0, 1, 2, 9, 31, 95, 168, 139, 32, 1, 0, 1, 2, 9, 31, 105, 248, 363, 224, 41, 1, 0, 1, 2, 9, 31, 108, 300, 614, 703, 350, 50, 1, 0

Offset: 0

Author

Alois P. Heinz, Oct 06 2016

Keywords

• nonn
• tabl

Examples

			Square array A(n,k) begins:
  1, 1,  1,   1,    1,    1,    1,    1,    1, ...
  0, 1,  2,   2,    2,    2,    2,    2,    2, ...
  0, 1,  5,   8,    9,    9,    9,    9,    9, ...
  0, 1,  8,  19,   27,   30,   31,   31,   31, ...
  0, 1, 13,  42,   74,   95,  105,  108,  109, ...
  0, 1, 18,  78,  168,  248,  300,  325,  335, ...
  0, 1, 25, 139,  363,  614,  814,  938, 1002, ...
  0, 1, 32, 224,  703, 1367, 1996, 2457, 2741, ...
  0, 1, 41, 350, 1297, 2879, 4642, 6128, 7168, ...
		

Links

• Alois P. Heinz, Antidiagonals n = 0..45, flattened

Crossrefs

Columns k=0-10 give: A000007, A000012, A000982(n+1), A101427, A277240, A277241, A277242, A277243, A277244, A277245, A277246.

Main diagonal gives A254686.

A(n,2n) gives A002774.