A260842 Sum of lcm(gcd(i,j), gcd(k,l)) for i,j,k,l in range [1..n].

1, 23, 136, 516, 1289, 3271, 5908, 11084, 18833, 31503, 44072, 71156, 93681, 133095, 190052, 256468, 311909, 421619, 501412, 664112, 847013, 1035763, 1186208, 1515000, 1790625, 2114575, 2502268, 3028600, 3354613, 4109163, 4517824, 5246624, 6070201, 6853807, 7933304

Offset: 1

Author

Sirius Caffrey, Aug 01 2015

Keywords

• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 161 terms from Robert G. Wilson v)
• Ren LuYao (FancyCoder), Round #49, BestCoder.

Programs

Maple

N:= 100: # to get a(1) to a(N)
M:= Matrix(N,N,igcd,shape=symmetric):
T:= Vector(N):
for n from 1 to N do
  T[M[n,n]]:= T[M[n,n]]+1;
  for j from 1 to n-1 do
    T[M[n,j]]:= T[M[n,j]]+2;
  od:
  A[n]:= 2*add(add(ilcm(i,j)*T[i]*T[j],i=1..j-1),j=2..n) + add(i*T[i]^2,i=1..n);
od:
seq(A[n],n=1..N); # Robert Israel, Aug 04 2015

Mathematica

f[n_] := Sum[ LCM[ GCD[i, j], GCD[k, l]], {i, n}, {j, n}, {k, n}, {l, n}]; Array[f, 35] (* Robert G. Wilson v, Aug 02 2015 *)

PARI

a(n) = {s = 0; for (i=1, n, for (j=1, n, for (k=1, n, for (l=1, n, s += lcm(gcd(i,j),gcd(k,l)););););); s;} \\ Michel Marcus, Aug 01 2015

Extensions

More terms from Michel Marcus, Aug 01 2015