A232533 a(n) = Sum_{i=1...n} Sum_{j=1..i} lcm(i,j)/i.

1, 3, 7, 13, 24, 35, 57, 79, 110, 142, 198, 237, 316, 381, 455, 541, 678, 770, 942, 1058, 1209, 1376, 1630, 1781, 2042, 2278, 2552, 2789, 3196, 3417, 3883, 4225, 4614, 5024, 5476, 5812, 6479, 6994, 7544, 7996, 8817, 9269, 10173, 10784, 11425, 12186, 13268

Offset

1,2

Comments

Partial sums of A057661.

Links

Table of n, a(n) for n=1..47.

Project Euler, Problem 448: Average least common multiple

Example

a(3) = lcm(1,1)/1 + (lcm(2,1) + lcm(2,2))/2 + (lcm(3,1) + lcm(3,2) + lcm(3,3))/3 = 7.

Mathematica

Table[Sum[Sum[LCM[m, k], {k, m}]/m, {m, n}], {n, 50}] (* T. D. Noe, Nov 25 2013 *)

Prog

(PARI) a(n)=sum(k=1, n, sum(b=1, k, lcm(b, k)/k));
(PARI) a(n)=sum(k=1, n, sum(m=1, k, m/gcd(m, k))); \\ Charles R Greathouse IV, Nov 25 2013

Crossrefs

Cf. A057661.

Sequence in context: A146606 A101302 A102948 * A061263 A156209 A076276

Adjacent sequences: A232530 A232531 A232532 * A232534 A232535 A232536

Keyword

nonn

Author

Zhining Yang, Nov 25 2013

Status

approved