A055934 a(0) = 1; a(n) = sum of a(j)'s, j<n, where n is divisible by a(j).

1, 1, 2, 2, 6, 2, 14, 2, 10, 2, 22, 2, 20, 2, 30, 2, 18, 2, 44, 2, 52, 2, 46, 2, 32, 2, 28, 2, 72, 2, 78, 2, 66, 2, 36, 2, 98, 2, 40, 2, 112, 2, 64, 2, 112, 2, 94, 2, 56, 2, 62, 2, 106, 2, 80, 2, 156, 2, 60, 2, 188, 2, 126, 2, 162, 2, 162, 2, 70, 2, 166, 2, 206, 2, 76, 2, 154, 2, 164, 2

Offset

0,3

Comments

a(2j+1) = 2 for j > 0; a(j) is even for j > 1.

Links

John Tyler Rascoe, Table of n, a(n) for n = 0..10000

Example

a(10) =22 because a(0), a(1), a(2), a(3), a(5), a(7), a(8) and a(9) all divide 10 and a(0) +a(1) +a(2) +a(3) +a(5) +a(7) +a(8) +a(9) = 1 + 1 +2 +2 +2 +2 + 10 +2 =22.

Prog

(Python)
def A055934_list(nmax):
    A = [1, 1]
    for n in range(2, nmax+1):
        if n%2 > 0:
            A.append(2)
        else:
            A.append(sum(i for i in A if n%i < 1))
    return A # John Tyler Rascoe, Jun 12 2024

Crossrefs

Cf. A055935.

Sequence in context: A278243 A071223 A249631 * A096217 A281145 A098555

Adjacent sequences: A055931 A055932 A055933 * A055935 A055936 A055937

Keyword

easy,nonn

Author

Leroy Quet, Jul 17 2000

Status

approved