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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.
1
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
1,1
COMMENTS
All terms are even (as the presence of 1 in a set does not change the least common multiple of its elements).
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).
EXAMPLE
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]
PROG
(PARI) row(n) = { my (d=divisors(n), r=vector(#d)); for (m=0, 2^#d-1, r[setsearch(d, lcm(vecextract(d, m)))]++); r }
CROSSREFS
Cf. A000005, A027750, A076078, A100587, A338508 (GCD variant).
Sequence in context: A285758 A340959 A246869 * A358947 A046663 A166594
KEYWORD
nonn,tabf
AUTHOR
Rémy Sigrist, Oct 31 2020
STATUS
approved