%I #8 Nov 02 2020 20:40:52

%S 2,2,2,2,2,2,2,4,2,2,2,2,2,10,2,2,2,2,4,8,2,2,4,2,2,2,10,2,2,2,2,2,4,

%T 10,44,2,2,2,2,2,10,2,2,2,10,2,2,4,8,16,2,2,2,2,2,10,4,44,2,2,2,2,4,2,

%U 10,44,2,2,2,10,2,2,2,10,2,2,2,2,2,4,10,8,44,184

%N Irregular table T(n, k) read by rows, n > 0 and k = 1..A000005(n); T(n, k) is the number of subsets of divisors of n with least common multiple of elements equal to the k-th divisor of n.

%C All terms are even (as the presence of 1 in a set does not change the least common multiple of its elements).

%F Sum_{k = 1..A000005(n)} T(n, k) = 1 + A100587(n).

%F T(n, A000005(n)) = A076078(n) for any n > 1.

%F T(n, 1) = 2.

%F T(n, k) = A338508(n, A000005(n)+1-k) for k = 2..A000005(n).

%e Triangle begins:

%e 1: [2]

%e 2: [2, 2]

%e 3: [2, 2]

%e 4: [2, 2, 4]

%e 5: [2, 2]

%e 6: [2, 2, 2, 10]

%e 7: [2, 2]

%e 8: [2, 2, 4, 8]

%e 9: [2, 2, 4]

%e 10: [2, 2, 2, 10]

%e 11: [2, 2]

%e 12: [2, 2, 2, 4, 10, 44]

%e 13: [2, 2]

%e 14: [2, 2, 2, 10]

%e 15: [2, 2, 2, 10]

%o (PARI) row(n) = { my (d=divisors(n), r=vector(#d)); for (m=0, 2^#d-1, r[setsearch(d, lcm(vecextract(d, m)))]++); r }

%Y Cf. A000005, A027750, A076078, A100587, A338508 (GCD variant).

%K nonn,tabf

%O 1,1

%A _Rémy Sigrist_, Oct 31 2020