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).

30, 3135, 60, 3570, 6279, 70, 844305, 7140, 8855, 90, 1231230, 1218945, 8970, 9405, 120

Offset: 3

Author

Paolo Xausa, May 07 2025

Keywords

• nonn
• tabl
• hard
• more

Examples

			Array begins:
  n\k|       1        2        3        4        5  ...
  -----------------------------------------------------
   3 |      30,      60,      70,      90,     120, ... = A365795
   4 |    3135,    6279,    8855,    9405,   10695, ... = A383728
   5 |    3570,    7140,    8970,   10626,   10710, ... = A383729
   6 |  844305, 1218945, 2496585, 2532915, 3024021, ...
   7 | 1231230, 2062830, 2181270, 2462460, 3327870, ...
  ...     |                                       \______ A383727 (main diagonal)
       A383725
		

Crossrefs

Cf. A001221, A365795, A382469, A383725, A383727, A383728, A383729.

Programs

Mathematica

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]]