A341270 a(n) = Sum_{k=1..n} a(n mod k) for n > 0; a(0) = 1.

1, 1, 2, 3, 4, 6, 7, 10, 12, 15, 17, 25, 24, 32, 37, 45, 46, 63, 62, 82, 83, 97, 104, 141, 130, 158, 170, 201, 202, 255, 242, 302, 306, 350, 367, 448, 416, 503, 522, 610, 597, 716, 690, 825, 832, 921, 945, 1147, 1085, 1255, 1272, 1430, 1435, 1683, 1631, 1888

Offset: 0

Author

Rok Cestnik, Feb 07 2021

Keywords

• nonn

Examples

			a(1) = a(1 mod 1) = a(0) = 1.
a(2) = a(2 mod 1)+a(2 mod 2) = a(0)+a(0) = 2.
a(3) = a(3 mod 1)+a(3 mod 2)+a(3 mod 3) = a(0)+a(1)+a(0) = 3.
		

Crossrefs

For Sum_{k=1..n} n mod k see A004125.

For Sum_{k=1..n} a(k) see A000079.

For Max_{k=1..n} a(n mod k)+1 see A113473.

Programs

Maple

a:= proc(n) option remember;
     `if`(n=0, 1, add(a(n mod k), k=1..n))
    end:
seq(a(n), n=0..62);  # Alois P. Heinz, Feb 07 2021

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[a[Mod[n, k]], {k, 1, n}]; Array[a, 50, 0] (* Amiram Eldar, Feb 08 2021 *)

PARI

a(n) = if (n==0, 1, sum(k=1, n, a(n % k))); \\ Michel Marcus, Feb 08 2021

Python

a = [1]
for n in range(1,1000):
    a.append(sum(a[n%k] for k in range(1,n+1)))