A377247 a(n) is the largest k such that the sum of the first k divisors of n is at most n.

1, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 4, 1, 3, 3, 4, 1, 4, 1, 4, 3, 3, 1, 6, 2, 3, 3, 5, 1, 6, 1, 5, 3, 3, 3, 6, 1, 3, 3, 6, 1, 6, 1, 5, 5, 3, 1, 7, 2, 5, 3, 5, 1, 6, 3, 6, 3, 3, 1, 9, 1, 3, 5, 6, 3, 6, 1, 5, 3, 6, 1, 9, 1, 3, 5, 5, 3, 6, 1, 8, 4, 3, 1, 9, 3, 3, 3, 6

Offset: 1

Author

David A. Corneth, Oct 21 2024

Keywords

• nonn

Examples

			a(1) = 1 as the sum of the first divisor of 1 is 1 <= 1 and 1 has no more divisors.
a(6) = 3 as the sum of the first three divisors is 1+2+3 <= 6 but the sum of the first four divisors is 1 + 2 + 3 + 6 = 12 > 6.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A081512, A117552 (corresponding sums).

Programs

Mathematica

A377247[n_] := LengthWhile[Accumulate[Divisors[n]], # <= n &];
Array[A377247, 100] (* Paolo Xausa, Aug 05 2025 *)

PARI

A377247(n) = {my(d = divisors(n), t = 0); for(i = 1, #d, t += d[i]; if(t > n, return(i-1))); 1}