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

0,8

Links

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

Example

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, ...

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.

Sequence in context: A145895 A114503 A103528 * A138352 A129620 A074766

Adjacent sequences: A277236 A277237 A277238 * A277240 A277241 A277242

Keyword

nonn,tabl

Author

Alois P. Heinz, Oct 06 2016

Status

approved