cp's OEIS Frontend

A338507 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.

%I A338507 #8 Nov 02 2020 20:40:52
%S A338507 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 A338507 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 A338507 10,44,2,2,2,10,2,2,2,10,2,2,2,2,2,4,10,8,44,184
%N A338507 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 A338507 All terms are even (as the presence of 1 in a set does not change the least common multiple of its elements).
%F A338507 Sum_{k = 1..A000005(n)} T(n, k) = 1 + A100587(n).
%F A338507 T(n, A000005(n)) = A076078(n) for any n > 1.
%F A338507 T(n, 1) = 2.
%F A338507 T(n, k) = A338508(n, A000005(n)+1-k) for k = 2..A000005(n).
%e A338507 Triangle begins:
%e A338507      1: [2]
%e A338507      2: [2, 2]
%e A338507      3: [2, 2]
%e A338507      4: [2, 2, 4]
%e A338507      5: [2, 2]
%e A338507      6: [2, 2, 2, 10]
%e A338507      7: [2, 2]
%e A338507      8: [2, 2, 4, 8]
%e A338507      9: [2, 2, 4]
%e A338507     10: [2, 2, 2, 10]
%e A338507     11: [2, 2]
%e A338507     12: [2, 2, 2, 4, 10, 44]
%e A338507     13: [2, 2]
%e A338507     14: [2, 2, 2, 10]
%e A338507     15: [2, 2, 2, 10]
%o A338507 (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 A338507 Cf. A000005, A027750, A076078, A100587, A338508 (GCD variant).
%K A338507 nonn,tabf
%O A338507 1,1
%A A338507 _Rémy Sigrist_, Oct 31 2020