A173185 Partial sums of A003418.

1, 2, 4, 10, 22, 82, 142, 562, 1402, 3922, 6442, 34162, 61882, 422242, 782602, 1142962, 1863682, 14115922, 26368162, 259160722, 491953282, 724745842, 957538402, 6311767282, 11665996162, 38437140562, 65208284962, 145521718162, 225835151362, 2554924714162

Offset: 0

Author

Jonathan Vos Post, Feb 12 2010

Keywords

• easy
• nonn

Comments

From Antti Karttunen, Feb 27 2014: (Start)

For all n >= 4, a(n) mod 10 = 2 (as A003418(5) = 60, the first multiple of ten in that sequence).

For all n >= 24, a(n) mod 100 = 62 (as A003418(25) = 26771144400, the first multiple of one hundred in that sequence).

Cf. also A236856.

a(n-1) gives the position of the first element of row n in irregular tables like A238280.

(End)

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2297 (first 251 terms from Antti Karttunen)

Crossrefs

One more than A236856.

Cf. A002944, A003418, A003422, A102910, A093880, A133233, A231721, A236857, A236858, A238280.

Programs

Maple

b:= proc(n) b(n):= `if`(n=0, 1, ilcm(n, b(n-1))) end:
a:= proc(n) a(n):= `if`(n<0, 0, a(n-1) +b(n)) end:
seq(a(n), n=0..35);  # Alois P. Heinz, Mar 31 2018

Mathematica

Table[If[n == 0, 1, LCM @@ Range[n]], {n, 0, 50}] // Accumulate (* Jean-François Alcover, Jan 03 2022 *)

PARI

a(n) = sum(k=0, n, lcm(vector(k, i, i))); \\ Michel Marcus, Mar 13 2018

Scheme

(define (A173185 n) (if (< n 1) 1 (+ (A173185 (- n 1)) (A003418 n))))

Formula

a(n) = Sum_{i=0..n} A003418(i).

Extensions

Missing term a(9)=3922 inserted by Antti Karttunen, Feb 27 2014