OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000 (first 1000 terms from Harry J. Smith)
FORMULA
a(n) = Sum_{i=1..tau(n)} (2*tau(n)-2*i+1)*d_i, where {d_i}, i=1..tau(n), is increasing sequence of divisors of n.
a(n) = Sum_{i=1..n} A135539(n,i)^2. - Ridouane Oudra, Oct 25 2021
EXAMPLE
a(6) = dot_product(7,5,3,1)*(1,2,3,6) = 7*1 + 5*2 + 3*3 + 1*6 = 32.
MAPLE
with(numtheory): seq(add((2*tau(n)-2*i+1)*sort(convert(divisors(n), 'list'))[i], i=1..tau(n)), n=1..200);
MATHEMATICA
Array[Function[{t, d}, Total@ MapIndexed[#1 (2 t - 2 First[#2] + 1) &, d]] @@ {DivisorSigma[0, #], Divisors[#]} &, 61] (* Michael De Vlieger, Oct 25 2021 *)
PROG
(PARI) { for (n=1, 1000, d=divisors(n); t=length(d); a=sum(i=1, t, (2*t - 2*i + 1)*d[i]); write("b064949.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 01 2009
(PARI) A064949(n) = { my(i=0, u=numdiv(n)); sumdiv(n, d, i++; (((2*u)-(2*i))+1)*d); }; \\ Antti Karttunen, Nov 14 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Oct 28 2001
STATUS
approved