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%I #18 Jul 02 2022 14:49:01
%S 1,1,1,1,2,1,1,2,3,1,1,4,3,4,1,1,2,9,4,5,1,1,4,3,16,5,6,1,1,2,9,4,25,
%T 6,7,1,1,8,3,16,5,36,7,8,1,1,4,27,4,25,6,49,8,9,1,1,4,9,64,5,36,7,64,
%U 9,10,1,1,2,9,16,125,6,49,8,81,10,11,1,1,8,3,16,25,216,7,64,9,100,11,12,1
%N Square array read by ascending antidiagonals: A(n,k) = k^Omega(n).
%H K. L. Verma, <a href="https://pjm.ppu.edu/sites/default/files/papers/PJM_May_2022_496_to_504.pdf">On an arithmetical functions involving general exponential</a>, Palestine Journal of Mathematics Vol. 11(2)(2022), 496-504.
%F A(n, k) = A051129(A001222(n), k).
%F The columns are totally multiplicative: A(i*j, k) = A(i, k)*A(j, k).
%e Array begins:
%e 1, 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 2, 3, 4, 5, 6, 7, 8, ...
%e 1, 2, 3, 4, 5, 6, 7, 8, ...
%e 1, 4, 9, 16, 25, 36, 49, 64, ...
%e 1, 2, 3, 4, 5, 6, 7, 8, ...
%e 1, 4, 9, 16, 25, 36, 49, 64, ...
%e 1, 2, 3, 4, 5, 6, 7, 8, ...
%e 1, 8, 27, 64, 125, 216, 343, 512, ...
%e ...
%t A[n_,k_]:=k^PrimeOmega[n]; Flatten[Table[A[n-k+1,k],{n,13},{k,n}]]
%Y Cf. A001222, A051129.
%Y Cf. A000012 (n = 1 or k = 1), A061142 (k = 2), A165824 - A165871 (k = 3..50), A176029 (diagonal).
%K nonn,tabl,easy
%O 1,5
%A _Stefano Spezia_, May 22 2022