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

1,3

Links

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

Example

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.

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 *)

Prog

(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;
}
(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

Crossrefs

Cf. A269427.

Sequence in context: A190177 A283764 A010603 * A328461 A341494 A210198

Adjacent sequences: A269420 A269421 A269422 * A269424 A269425 A269426

Keyword

easy,nonn

Author

Alec Jones, Feb 25 2016

Status

approved