A269423 a(n) is the sum of all 0 < m < n for which n == a(m) (mod m).

1, 1, 3, 1, 7, 4, 8, 8, 10, 16, 3, 9, 7, 12, 13, 25, 12, 4, 12, 14, 22, 58, 3, 12, 34, 48, 11, 31, 31, 4, 79, 14, 35, 82, 36, 113, 21, 28, 6, 47, 59, 9, 46, 1, 105, 131, 59, 103, 30, 27, 48, 12, 7, 38, 60, 19, 50, 110, 157, 210, 7, 6, 23, 134

Offset: 1

Author

Alec Jones, Feb 25 2016

Keywords

• easy
• nonn

Examples

			We define a(1) = 1.
a(2) = 1, because 2 == a(1) (mod 1);
a(3) = 3, because 3 == a(1) (mod 1), and 3 == a(2) (mod 2): 1 + 2 = 3;
a(4) = 1, because 4 == a(1) (mod 1);
a(5) = 7, because 5 == 1 (mod 1), 5 == a(2) (mod 2), and 5 == a(4) (mod 4): 1 + 2 + 4 = 7.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A269427.

Programs

Java

int[] terms = new int[100];
terms[0] = 1;
for (int i = 1; i < 100; i++) {
    int count = 0;
    for (int j = 0; j < i; j++) {
        if (((i+1) - terms[j]) % (j+1) == 0) {
            count = count + j + 1;
        }
    }
    terms[i] = count;
}

Mathematica

a = {1}; Do[AppendTo[a, Total@ Select[Range[n - 1], Mod[n, #] == Mod[a[[#]], #] &]], {n, 2, 64}]; a (* Michael De Vlieger, Mar 24 2016 *)

PARI

lista(nn) = {va = vector(nn); print1(va[1] = 1, ", "); for (n=2, nn, va[n] = sum(m=1, n-1, m*(Mod(va[m], m) == Mod(n, m))); print1(va[n], ", "););} \\ Michel Marcus, Feb 26 2016