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.

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, 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, 10, 44, 2, 2, 2, 10, 2, 2, 2, 10, 2, 2, 2, 2, 2, 4, 10, 8, 44, 184

Offset: 1

Author

Rémy Sigrist, Oct 31 2020

Keywords

• nonn
• tabf

Comments

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

Examples

			Triangle begins:
     1: [2]
     2: [2, 2]
     3: [2, 2]
     4: [2, 2, 4]
     5: [2, 2]
     6: [2, 2, 2, 10]
     7: [2, 2]
     8: [2, 2, 4, 8]
     9: [2, 2, 4]
    10: [2, 2, 2, 10]
    11: [2, 2]
    12: [2, 2, 2, 4, 10, 44]
    13: [2, 2]
    14: [2, 2, 2, 10]
    15: [2, 2, 2, 10]
		

Crossrefs

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

Programs

PARI

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

Formula

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

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

T(n, 1) = 2.

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