A269427 -id:A269427 - cp's OEIS frontend

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

Alec Jones, Feb 25 2016

			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.

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

Cf. A269427.

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;
}

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

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

A271773 a(1) = 0, then a(n) is the maximum of all 0 < m < n for which n == a(m) (mod m).

Original entry on oeis.org

0, 1, 2, 1, 4, 1, 6, 3, 5, 1, 10, 1, 12, 9, 2, 1, 16, 1, 18, 7, 11, 1, 22, 5, 13, 3, 20, 1, 28, 1, 30, 21, 17, 7, 8, 1, 36, 25, 5, 1, 40, 1, 42, 39, 23, 1, 46, 7, 16, 33, 14, 1, 52, 11, 48, 19, 29, 1, 58, 1, 60, 15, 38, 13, 54, 1, 66, 45, 7, 1, 70, 1, 72, 27

Offset: 1

Peter Kagey, Apr 14 2016

nonn

			a(1) = 0 by definition.
a(2) = 1 because a(1) == 2 (mod 1).
a(3) = 2 because a(2) == 3 (mod 2).
a(4) = 1 because a(1) == 4 (mod 1).
a(5) = 4 because a(4) == 5 (mod 4).
a(6) = 1 because a(1) == 6 (mod 1).
a(7) = 6 because a(6) == 7 (mod 6).
a(8) = 3 because a(3) == 8 (mod 3).

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

Cf. A269423, A269427, A271530, A271531, A271774.

a[1] = 0; a[n_] := a[n] = Max@ Select[Range[n - 1], Mod[n, #] == Mod[a[#], #] &]; Table[a@ n, {n, 75}] (* Michael De Vlieger, Apr 15 2016 *)

cp's OEIS Frontend

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

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