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A269423 a(n) is the sum of all 0 < m < n for which n == a(m) (mod m). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 5 20:57 EST 2023. Contains 360087 sequences. (Running on oeis4.)