A064946 a(n) = Sum_{i|n, j|n, j>i} j.

0, 2, 3, 10, 5, 26, 7, 34, 21, 42, 11, 104, 13, 58, 58, 98, 17, 152, 19, 165, 80, 90, 23, 324, 55, 106, 102, 227, 29, 397, 31, 258, 124, 138, 124, 575, 37, 154, 146, 507, 41, 544, 43, 351, 325, 186, 47, 892, 105, 392, 190, 413, 53, 692, 192, 693, 212, 234, 59

Offset: 1

Author

Vladeta Jovovic, Oct 28 2001

Keywords

• nonn

Examples

			a(6) = dot_product(0,1,2,3)*(1,2,3,6) = 0*1 + 1*2 + 2*3 + 3*6 = 26.
		

Links

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

Crossrefs

Cf. A064944, A064945, A064947, A064948, A064949.

Cf. A000005, A000203, A064840, A337297, A027750.

Programs

Maple

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

Mathematica

A064946[n_] := #.Range[Length[#]] & [Rest[Divisors[n]]];
Array[A064946, 100] (* Paolo Xausa, Aug 14 2025 *)

PARI

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

Formula

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

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

From Ridouane Oudra, Aug 06 2025: (Start)

a(n) = A064948(n) - A064944(n).

a(n) = A064840(n) - A064945(n).

a(n) = A337297(n) - A064947(n).

a(n) = (A064948(n) - A000203(n))/2. (End)