A064945 a(n) = Sum_{i|n, j|n, j >= i} i.

1, 4, 5, 11, 7, 22, 9, 26, 18, 30, 13, 64, 15, 38, 38, 57, 19, 82, 21, 87, 48, 54, 25, 156, 38, 62, 58, 109, 31, 179, 33, 120, 68, 78, 68, 244, 39, 86, 78, 213, 43, 224, 45, 153, 143, 102, 49, 348, 66, 166, 98, 175, 55, 268, 96, 267, 108, 126, 61, 542, 63, 134, 181

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

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

From Ridouane Oudra, Aug 02 2025: (Start)

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

a(n) = A064947(n) + A000203(n).

a(n) = (A064949(n) + A000203(n))/2.

a(n) = A064949(n) - A064947(n).

a(n) = A337360(n) - A064944(n).

a(n) = A064840(n) - A064946(n). (End)

Example

a(6) = dot_product(4,3,2,1)*(1,2,3,6) = 4*1+3*2+2*3+1*6 = 22.

Maple

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

Mathematica

A064945[n_] := #.Range[Length[#], 1, -1] & [Divisors[n]];
Array[A064945, 100] (* Paolo Xausa, Aug 07 2025 *)

Prog

(PARI) a(n) = my(d=divisors(n), t=length(d)); sum(i=1, t, (t - i + 1)*d[i]); \\ Harry J. Smith, Oct 01 2009
(PARI) a(n)=my(d=divisors(n)); sum(i=1, #d, (#d+1-i)*d[i]) \\ Charles R Greathouse IV, Jun 10 2015
(Haskell)
a064945 = sum . zipWith (*) [1..] . reverse . a027750_row'
-- Reinhard Zumkeller, Jul 14 2015
(Python)
from sympy import divisors, divisor_sigma
def A064945(n): return (divisor_sigma(n, 0)+1)*divisor_sigma(n)-sum(a*b for a, b in enumerate(divisors(n), 1)) # Chai Wah Wu, Aug 07 2025

Crossrefs

Cf. A060640, A064944, A064946, A064947, A064948, A064949.

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

Cf. A386911.

Sequence in context: A322655 A206028 A007429 * A069820 A318446 A317304

Adjacent sequences: A064942 A064943 A064944 * A064946 A064947 A064948

Keyword

nonn,easy

Author

Vladeta Jovovic, Oct 28 2001

Status

approved