A064948 a(n) = Sum_{i|n, j|n} max(i,j).

1, 7, 10, 27, 16, 64, 22, 83, 55, 102, 34, 236, 40, 140, 140, 227, 52, 343, 58, 372, 192, 216, 70, 708, 141, 254, 244, 510, 88, 866, 94, 579, 296, 330, 296, 1241, 112, 368, 348, 1104, 124, 1184, 130, 786, 728, 444, 142, 1908, 267, 877, 452, 924, 160, 1504, 456

Offset: 1

Author

Vladeta Jovovic, Oct 28 2001

Keywords

• nonn

Examples

			a(6) = dot_product(1,3,5,7)*(1,2,3,6) = 1*1 + 3*2 + 5*3 + 7*6 = 64.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000203, A064944, A064840.

Programs

Maple

with(numtheory): seq(add((2*i-1)*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);

Mathematica

A064948[n_] := #.(2*Range[Length[#]] - 1) & [Divisors[n]];
Array[A064948, 100] (* Paolo Xausa, Aug 14 2025 *)

PARI

a(n) = { my(d=divisors(n)); sum(i=1, #d, (2*i - 1)*d[i]) } \\ Harry J. Smith, Oct 01 2009

Formula

a(n) = Sum_{i=1..tau(n)} (2*i-1)*d_i, where {d_i}, i=1..tau(n), is the increasing sequence of the divisors of n.

a(n) = 2*A064944(n) - A000203(n). - Amiram Eldar, Dec 23 2024

From Ridouane Oudra, Aug 07 2025: (Start)

a(n) = A064944(n) + A064946(n).

a(n) = 2*A064946(n) + A000203(n).

a(n) = 2*A064840(n) - A064949(n). (End)