A367628 Sum of the divisors of n <= tau(n).

1, 3, 1, 3, 1, 6, 1, 7, 4, 3, 1, 16, 1, 3, 4, 7, 1, 12, 1, 12, 4, 3, 1, 24, 1, 3, 4, 7, 1, 17, 1, 7, 4, 3, 1, 25, 1, 3, 4, 20, 1, 19, 1, 7, 9, 3, 1, 24, 1, 8, 4, 7, 1, 12, 1, 22, 4, 3, 1, 43, 1, 3, 4, 7, 1, 12, 1, 7, 4, 15, 1, 45, 1, 3, 9, 7, 1, 12, 1, 30, 4, 3, 1, 35, 1

Offset

1,2

Comments

First differs from A126212(n) at a(25) = 1.

Links

Table of n, a(n) for n=1..85.

Formula

a(n) = Sum_{d|n, d<=tau(n)} d.

Example

a(12) = 16. The sum of the divisors of 12 <= tau(12) = 6 are 1 + 2 + 3 + 4 + 6 = 16.

Mathematica

Table[Sum[k(1-Ceiling[n/k]+Floor[n/k]), {k, DivisorSigma[0, n]}], {n, 100}]

Prog

(PARI) a(n) = my(t=numdiv(n)); sumdiv(n, d, if (d <=t, d)); \\ Michel Marcus, Nov 25 2023

Crossrefs

Cf. A000005 (tau), A126212, A366979.

Sequence in context: A236865 A236829 A236800 * A126212 A357858 A066637

Adjacent sequences: A367625 A367626 A367627 * A367629 A367630 A367631

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 24 2023

Status

approved