A338507 - OEIS

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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.

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

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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).

LINKS

Table of n, a(n) for n=1..84.

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

Adjacent sequences: A338504 A338505 A338506 * A338508 A338509 A338510

KEYWORD

nonn,tabf

AUTHOR

Rémy Sigrist, Oct 31 2020

STATUS

approved