A120877 a(1) = 1. a(n) = number of earlier terms of the sequence that divide the sum of the earlier terms of the sequence.

1, 1, 2, 3, 2, 3, 6, 7, 2, 4, 2, 4, 2, 4, 2, 4, 3, 12, 12, 12, 12, 12, 13, 2, 2, 5, 10, 23, 2, 3, 15, 2, 7, 18, 12, 12, 14, 32, 16, 31, 2, 6, 6, 9, 20, 13, 7, 13, 2, 2, 6, 6, 7, 17, 6, 6, 8, 2, 6, 3, 16, 19, 9, 32, 16, 33, 9, 45, 10, 3, 19, 5, 16, 20, 20, 35, 4, 8, 2, 3, 17, 19, 17, 19, 22, 35

Offset

1,3

Comments

Sum of first n terms of this sequence is A120878(n).

Links

Samuel B. Reid, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^16, showing first appearances of number k in red, and repeated appearances of number k in blue.

Example

The sum of the first 9 terms of the sequence is 27. Among the first 9 terms of the sequence there are 4 terms (a(1)=1, a(2)=1, a(4)=3, a(6)=3) which divide 27.
So a(10) = 4.

Mathematica

s={1}; Do[ ct=0; sm=Total[s]; Do[If[Divisible[sm, s[[j]]], ct++] , {j, n-1}]; AppendTo[s, ct], {n, 2, 86}]; s (* James C. McMahon, Oct 12 2024 *)

Prog

(PARI) {m=86; print1(a=1, ", "); v=[a]; for(n=2, m, a=0; q=sum(i=1, n-1, v[i]); for(j=1, n-1, if(q%v[j]==0, a++)); print1(a, ", "); v=concat(v, a))} \\ Klaus Brockhaus, Aug 16 2006

Crossrefs

Cf. A120878.

Sequence in context: A300500 A339132 A064895 * A326304 A174091 A318789

Adjacent sequences: A120874 A120875 A120876 * A120878 A120879 A120880

Keyword

nonn

Author

Leroy Quet, Jul 10 2006

Extensions

More terms from Klaus Brockhaus, Aug 16 2006

Status

approved