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

1,2

Links

Table of n, a(n) for n=1..49.

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.

Example

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

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 *)

Crossrefs

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

Sequence in context: A391995 A301284 A364685 * A024983 A009896 A027372

Adjacent sequences: A382066 A382067 A382068 * A382070 A382071 A382072

Keyword

nonn

Author

Ctibor O. Zizka, Mar 14 2025

Status

approved