A064951 a(n) = Sum_{1 <= x, y <= n} lcm(x, y).

1, 7, 28, 72, 177, 303, 604, 948, 1497, 2127, 3348, 4272, 6313, 8119, 10324, 13060, 17701, 20995, 27512, 32132, 38453, 45779, 57440, 64664, 77689, 89935, 104704, 117948, 141525, 154755, 183616, 205472, 231113, 258959, 290564, 314720, 364041

Offset: 1

Author

Vladeta Jovovic, Oct 28 2001

Keywords

• nonn

Comments

a(n) is also the entrywise 1-norm of the n X n LCM matrix.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A018806, A051193, A057660.

Programs

Mathematica

Table[nn = n;Total[Level[Table[Table[LCM[i, j], {i, 1, nn}], {j, 1, nn}], {2}]], {n, 1, 37}] (* Geoffrey Critzer, Jan 14 2015 *)

PARI

{ a=0; for (n=1, 1000, a+=n*sum(k=1, n, n/gcd(n, k)); write("b064951.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 01 2009

Formula

a(n) = a(n-1) + 2*A051193(n) - n = a(n-1) + n*A057660(n) = Sum_{1 <= i <= j <= n} (j^2/gcd(i, j)). - Henry Bottomley, Oct 29 2001

a(n) ~ 3 * zeta(3) * n^4 / (2*Pi^2). - Vaclav Kotesovec, May 29 2021