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a(n) = Sum_{i|n, j|n} max(i,j).
1

%I #14 Dec 23 2024 09:54:39

%S 1,7,10,27,16,64,22,83,55,102,34,236,40,140,140,227,52,343,58,372,192,

%T 216,70,708,141,254,244,510,88,866,94,579,296,330,296,1241,112,368,

%U 348,1104,124,1184,130,786,728,444,142,1908,267,877,452,924,160,1504,456

%N a(n) = Sum_{i|n, j|n} max(i,j).

%H Harry J. Smith, <a href="/A064948/b064948.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = Sum_{i=1..tau(n)} (2*i-1)*d_i, where {d_i}, i=1..tau(n), is the increasing sequence of the divisors of n.

%F a(n) = 2*A064944(n) - A000203(n). - _Amiram Eldar_, Dec 23 2024

%e a(6) = dot_product(1,3,5,7)*(1,2,3,6) = 1*1 + 3*2 + 5*3 + 7*6 = 64.

%p with(numtheory): seq(add((2*i-1)*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);

%o (PARI) { for (n=1, 1000, d=divisors(n); a=sum(i=1, length(d), (2*i - 1)*d[i]); write("b064948.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 01 2009

%Y Cf. A000005, A000203, A064944.

%K nonn

%O 1,2

%A _Vladeta Jovovic_, Oct 28 2001