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

1,2

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.

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 *)

Prog

(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

Crossrefs

Sequence in context: A039613 A009482 A191745 * A093806 A142679 A254758

Adjacent sequences: A260839 A260840 A260841 * A260843 A260844 A260845

Keyword

nonn

Author

Sirius Caffrey, Aug 01 2015

Extensions

More terms from Michel Marcus, Aug 01 2015

Status

approved