OFFSET
1,2
COMMENTS
Does every positive integer except 2 and 5 occur here? The stronger form of Goldbach's conjecture (every even integer > 6 is the sum of two distinct primes) suffices to show that every odd integer (except 5) is in the sequence, since T(p,q) = p + q + 1.
LINKS
Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
FORMULA
T(n,k) = sigma(n) + sigma(k) - sigma(gcd(n,k)).
EXAMPLE
Triangle begins:
1
3 3
4 6 4
7 7 10 7
6 8 9 12 6
12 12 12 16 17 12
...
The divisors of 3 are {1, 3}; the divisors of 4 are {1, 2, 4}. The union is {1, 2, 3, 4}, summing to 10; so T(4,3) = 10.
MAPLE
seq(seq(numtheory:-sigma(n) + numtheory:-sigma(k) - numtheory:-sigma(igcd(n, k)), k=1..n), n=1..10); # Robert Israel, Dec 17 2015
MATHEMATICA
Table[Total@ Union[Divisors@ n, Divisors@ k], {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Dec 18 2015 *)
PROG
(PARI) T(n, k) = sigma(n) + sigma(k) - sigma(gcd(n, k))
(Haskell)
a265652 n k = a265652_tabl !! (n-1) !! (k-1)
a265652_row n = a265652_tabl !! (n-1)
a265652_tabl = zipWith (zipWith (-))
(zipWith (map . (+)) a000203_list a245093_tabl) a132442_tabl
-- Reinhard Zumkeller, Dec 12 2015
CROSSREFS
AUTHOR
Franklin T. Adams-Watters, Dec 11 2015
STATUS
approved