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A173185
Partial sums of A003418.
3
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
0,2
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)
FORMULA
a(n) = Sum_{i=0..n} A003418(i).
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 *)
PROG
(Scheme) (define (A173185 n) (if (< n 1) 1 (+ (A173185 (- n 1)) (A003418 n))))
(PARI) a(n) = sum(k=0, n, lcm(vector(k, i, i))); \\ Michel Marcus, Mar 13 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 12 2010
EXTENSIONS
Missing term a(9)=3922 inserted by Antti Karttunen, Feb 27 2014
STATUS
approved