A382069 Row sums of the triangular array in A199408.

1, 4, 10, 18, 31, 42, 64, 80, 105, 128, 166, 182, 235, 262, 300, 344, 409, 432, 514, 538, 607, 674, 760, 776, 885, 952, 1026, 1086, 1219, 1230, 1396, 1440, 1545, 1652, 1738, 1794, 1999, 2074, 2176, 2240, 2461, 2472, 2710, 2758, 2871, 3062, 3244, 3240, 3493

Offset: 1

Author

Ctibor O. Zizka, Mar 14 2025

Keywords

• nonn

Examples

			n = 3: a(3) = 3 + 4 + 3 = 10.
n = 4: a(4) = 4 + 4 + 6 + 4 = 18.
		

Crossrefs

Cf. A000040, A000217, A000290, A001248, A006093, A018804, A040976, A087397, A199408.

Programs

Mathematica

f[p_, e_] := (e*(p-1)/p + 1) * p^e; a[n_] := n*(3*n+1)/2 - Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Mar 14 2025 *)

Formula

a(n) = A000217(n) + A000290(n) - A018804(n).

a(A000040(n)) = A001248(n) + A006093(n)*A040976(n)/2.

a(A000040(n)) = A001248(n) + A087397(n) for n > 2.