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A383726 Square array read by ascending antidiagonals, where row n lists numbers m such that omega(m) = n and the largest prime factor of m equals the sum of its remaining distinct prime factors, where omega(m) = A001221(m).

%I A383726 #11 May 11 2025 11:56:35
%S A383726 30,3135,60,3570,6279,70,844305,7140,8855,90,1231230,1218945,8970,
%T A383726 9405,120
%N A383726 Square array read by ascending antidiagonals, where row n lists numbers m such that omega(m) = n and the largest prime factor of m equals the sum of its remaining distinct prime factors, where omega(m) = A001221(m).
%e A383726 Array begins:
%e A383726   n\k|       1        2        3        4        5  ...
%e A383726   -----------------------------------------------------
%e A383726    3 |      30,      60,      70,      90,     120, ... = A365795
%e A383726    4 |    3135,    6279,    8855,    9405,   10695, ... = A383728
%e A383726    5 |    3570,    7140,    8970,   10626,   10710, ... = A383729
%e A383726    6 |  844305, 1218945, 2496585, 2532915, 3024021, ...
%e A383726    7 | 1231230, 2062830, 2181270, 2462460, 3327870, ...
%e A383726   ...     |                                       \______ A383727 (main diagonal)
%e A383726        A383725
%t A383726 Module[{dmax = 5, a, m}, a = Table[m = Times @@ Prime[Range[n]] - 1; Table[While[Length[#] != n || Total[Most[#]] != Last[#] & [FactorInteger[++m][[All,1]]]]; m, dmax-n+3], {n, dmax+2, 3, -1}]; Array[Diagonal[a, # - dmax] &, dmax]]
%Y A383726 Cf. A001221, A365795, A382469, A383725, A383727, A383728, A383729.
%K A383726 nonn,tabl,hard,more
%O A383726 3,1
%A A383726 _Paolo Xausa_, May 07 2025