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

1,4

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

Links

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

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.

Example

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

Maple

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

Prog

(PARI) { for (n=1, 1000, d=divisors(n); t=length(d); a=sum(i=1, t - 1, (t - i)*d[i]); write("b064947.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 01 2009

Crossrefs

Cf. A000005, A000203.

Sequence in context: A348184 A065045 A185088 * A369894 A059926 A306546

Adjacent sequences: A064944 A064945 A064946 * A064948 A064949 A064950

Keyword

nonn

Author

Vladeta Jovovic, Oct 28 2001

Status

approved