A373113 For n >= 1, a(n) = Sum_{i = n..(n + A000005(n) - 1)} i.

1, 5, 7, 15, 11, 30, 15, 38, 30, 46, 23, 87, 27, 62, 66, 90, 35, 123, 39, 135, 90, 94, 47, 220, 78, 110, 114, 183, 59, 268, 63, 207, 138, 142, 146, 360, 75, 158, 162, 348, 83, 364, 87, 279, 285, 190, 95, 525, 150, 315, 210, 327, 107, 460, 226, 476, 234, 238, 119, 786, 123

Offset: 1

Author

Ctibor O. Zizka, May 25 2024

Keywords

• nonn

Comments

A005385 is a subsequence.

Examples

			n = 4: A000005(4) = 3, 4 + 5 + 6 = 15, thus a(4) = 15.
n = 5: A000005(5) = 2, 5 + 6 = 11, thus a(5) = 11.
n = 6: A000005(6) = 4, 6 + 7 + 8 + 9 = 30, thus a(6) = 30.
		

Crossrefs

Cf. A000005, A005384, A005385, A066446.

Programs

Mathematica

a[n_] := Module[{d = DivisorSigma[0, n]}, d*(d-1)/2 + n*d]; Array[a, 60] (* Amiram Eldar, May 25 2024 *)

PARI

a(n) = my(d=numdiv(n)); n*d + d*(d-1)/2; \\ Michel Marcus, May 28 2024

Formula

a(n) = A066446(n) + n*A000005(n).

a(n) = A000005(n)*(A000005(n) - 1)/2 + n*A000005(n).