A064947 a(n) = Sum_{i|n, j|n, j>i} i.

0, 1, 1, 4, 1, 10, 1, 11, 5, 12, 1, 36, 1, 14, 14, 26, 1, 43, 1, 45, 16, 18, 1, 96, 7, 20, 18, 53, 1, 107, 1, 57, 20, 24, 20, 153, 1, 26, 22, 123, 1, 128, 1, 69, 65, 30, 1, 224, 9, 73, 26, 77, 1, 148, 24, 147, 28, 36, 1, 374, 1, 38, 77, 120, 26, 168, 1, 93, 32, 165, 1, 411, 1, 44

Offset: 1

Author

Vladeta Jovovic, Oct 28 2001

Keywords

• nonn

Comments

For given n, iterate a(n); a(a(n)); a(a(a(n))); ... Does this iterative process always lead to a(a(...(a(n))...)) = 1? - Ctibor O. Zizka, Apr 17 2008

No. For example, a(4) = 4, a(14) = 14, and a(99) = 99. - Jason Yuen, Jan 07 2025

Examples

			a(6) = dot_product(3,2,1,0)*(1,2,3,6) = 3*1 + 2*2 + 1*3 + 0*6 = 10.
		

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

Table[t = DivisorSigma[0, n]; Total@ MapIndexed[(t - First[#2])*#1 &, Divisors[n]], {n, 120}] (* Michael De Vlieger, Jan 07 2025 *)

PARI

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

Formula

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

From Ridouane Oudra, Aug 07 2025: (Start)

a(n) = A064945(n) - A000203(n).

a(n) = A064840(n) - A064944(n).

a(n) = A064949(n) - A064945(n).

a(n) = A337297(n) - A064946(n).

a(n) = (A064949(n) - A000203(n))/2. (End)