A269423 - OEIS

%I #19 Apr 04 2016 00:28:46

%S 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,

%T 31,31,4,79,14,35,82,36,113,21,28,6,47,59,9,46,1,105,131,59,103,30,27,

%U 48,12,7,38,60,19,50,110,157,210,7,6,23,134

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

%H Peter Kagey, <a href="/A269423/b269423.txt">Table of n, a(n) for n = 1..10000</a>

%e We define a(1) = 1.

%e a(2) = 1, because 2 == a(1) (mod 1);

%e a(3) = 3, because 3 == a(1) (mod 1), and 3 == a(2) (mod 2): 1 + 2 = 3;

%e a(4) = 1, because 4 == a(1) (mod 1);

%e a(5) = 7, because 5 == 1 (mod 1), 5 == a(2) (mod 2), and 5 == a(4) (mod 4): 1 + 2 + 4 = 7.

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

%o (Java)

%o int[] terms = new int[100];

%o terms[0] = 1;

%o for (int i = 1; i < 100; i++) {

%o     int count = 0;

%o     for (int j = 0; j < i; j++) {

%o         if (((i+1) - terms[j]) % (j+1) == 0) {

%o             count = count + j + 1;

%o         }

%o     }

%o     terms[i] = count;

%o }

%o (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

%Y Cf. A269427.

%K easy,nonn

%O 1,3

%A _Alec Jones_, Feb 25 2016