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User: Sirius Caffrey

Sirius Caffrey has authored 2 sequences.

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

Sirius Caffrey, Aug 01 2015

nonn

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.

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

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 *)

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

More terms from Michel Marcus, Aug 01 2015

A260185 a(n) is the number of ways to select an ordered pair of subsets of {2,...,n} such that each pair of elements from different subsets are relatively prime.

Original entry on oeis.org

1, 3, 9, 21, 63, 111, 333, 693, 1521, 2577, 7731, 13491, 40473, 67833, 119241, 239481, 718443, 1340523, 4021569, 7494849, 13356657, 22271409, 66814227, 130266387, 268286823, 447212583, 896472063, 1684872063, 5054616189, 9566769789, 28700309367, 57402497367

Offset: 1

Sirius Caffrey, Jul 17 2015

nonn

This sequence was used by LuoYuping when he set a problem for NOI 2015 Day1 Problem3.

a(n) is the number of ways to find X and Y where set X and Y are subsets of {2,...,n}, and for all a in X and all b in Y, gcd(a,b) = 1. Also note that X or Y can be empty.

			For n=1 the 1 pair of sets is [{},{}].
For n=2 the 3 pairs of sets are [{},{}], [{2},{}], and [{},{2}].
For n=3 the 9 pairs of sets are [{},{}], [{2},{}], [{},{2}], [{3},{}], [{},{3}], [{2,3},{}], [{},{2,3}], [{2},{3}], and [{3},{2}].

National Olympiad in Informatics 2015, China, Day 1 Problem 3.

Alois P. Heinz, Table of n, a(n) for n = 1..100 (first 80 terms from Giovanni Resta)
Sirius Caffrey, C++ program for A260185
Sirius Caffrey, Python program for A260185

Python
```
#  see link above
```

a(p) = 3*a(p-1) for p prime. - Alois P. Heinz, Jul 19 2015

a(31)-a(32) from Giovanni Resta, Jul 18 2015

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User: Sirius Caffrey

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

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A260185 a(n) is the number of ways to select an ordered pair of subsets of {2,...,n} such that each pair of elements from different subsets are relatively prime.

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