A064944 a(n) = Sum_{i|n, j|n, j >= i} j.

1, 5, 7, 17, 11, 38, 15, 49, 34, 60, 23, 132, 27, 82, 82, 129, 35, 191, 39, 207, 112, 126, 47, 384, 86, 148, 142, 283, 59, 469, 63, 321, 172, 192, 172, 666, 75, 214, 202, 597, 83, 640, 87, 435, 403, 258, 95, 1016, 162, 485, 262, 511, 107, 812, 264, 813, 292, 324

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Formula

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

a(n) = Sum_{i=1..A000005(n)} i*A027750(n, i). - Michel Marcus, Jun 10 2015

From Ridouane Oudra, Aug 01 2025: (Start)

a(n) = Sum_{d|n} (n/d)*A135539(n,d).

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

a(n) = (A064948(n) + A000203(n))/2.

a(n) = A337360(n) - A064945(n).

a(n) = A064948(n) - A064946(n).

a(n) = A064840(n) - A064947(n). (End)

Example

a(6) = max(1,1)+max(1,2)+max(1,3)+max(1,6)+max(2,2)+max(2,3)+max(2,6)+max(3,3)+max(3,6)+max(6,6)=38, or a(6) = dot_product(1,2,3,4)*(1,2,3,6)=1*1+2*2+3*3+4*6=38.

Maple

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

Mathematica

A064944[n_] := #.Range[Length[#]] & [Divisors[n]];
Array[A064944, 100] (* Paolo Xausa, Aug 07 2025 *)

Prog

(PARI) a(n) = my(d=divisors(n)); sum(i=1, length(d), i*d[i]); \\ Harry J. Smith, Sep 30 2009
(Haskell)
a064944 = sum . zipWith (*) [1..] . a027750_row'
-- Reinhard Zumkeller, Jul 14 2015
(Python)
from sympy import divisors
def A064944(n): return sum(a*b for a, b in enumerate(divisors(n), 1)) # Chai Wah Wu, Aug 07 2025

Crossrefs

Cf. A060640, A064945, A064946, A064947, A064948, A064949.

Cf. A027750, A135539, A000005, A000203, A064840, A337360, A337297.

Sequence in context: A374777 A318491 A060640 * A341038 A070372 A082818

Adjacent sequences: A064941 A064942 A064943 * A064945 A064946 A064947

Keyword

nonn

Author

Vladeta Jovovic, Oct 28 2001

Status

approved