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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.

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%I A277239 #12 Oct 18 2018 16:51:51
%S A277239 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,
%T A277239 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,
%U A277239 105,248,363,224,41,1,0,1,2,9,31,108,300,614,703,350,50,1,0
%N 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.
%H A277239 Alois P. Heinz, <a href="/A277239/b277239.txt">Antidiagonals n = 0..45, flattened</a>
%e A277239 Square array A(n,k) begins:
%e A277239   1, 1,  1,   1,    1,    1,    1,    1,    1, ...
%e A277239   0, 1,  2,   2,    2,    2,    2,    2,    2, ...
%e A277239   0, 1,  5,   8,    9,    9,    9,    9,    9, ...
%e A277239   0, 1,  8,  19,   27,   30,   31,   31,   31, ...
%e A277239   0, 1, 13,  42,   74,   95,  105,  108,  109, ...
%e A277239   0, 1, 18,  78,  168,  248,  300,  325,  335, ...
%e A277239   0, 1, 25, 139,  363,  614,  814,  938, 1002, ...
%e A277239   0, 1, 32, 224,  703, 1367, 1996, 2457, 2741, ...
%e A277239   0, 1, 41, 350, 1297, 2879, 4642, 6128, 7168, ...
%Y A277239 Columns k=0-10 give: A000007, A000012, A000982(n+1), A101427, A277240, A277241, A277242, A277243, A277244, A277245, A277246.
%Y A277239 Main diagonal gives A254686.
%Y A277239 A(n,2n) gives A002774.
%K A277239 nonn,tabl
%O A277239 0,8
%A A277239 _Alois P. Heinz_, Oct 06 2016