A338508 Irregular table T(n, k) read by rows, n > 0 and k = 1..A000005(n); T(n, k) is the number of nonempty subsets of divisors of n with greatest common divisor of elements equal to the k-th divisor of n.

1, 2, 1, 2, 1, 4, 2, 1, 2, 1, 10, 2, 2, 1, 2, 1, 8, 4, 2, 1, 4, 2, 1, 10, 2, 2, 1, 2, 1, 44, 10, 4, 2, 2, 1, 2, 1, 10, 2, 2, 1, 10, 2, 2, 1, 16, 8, 4, 2, 1, 2, 1, 44, 4, 10, 2, 2, 1, 2, 1, 44, 10, 2, 4, 2, 1, 10, 2, 2, 1, 10, 2, 2, 1, 2, 1, 184, 44, 8, 10, 4, 2, 2, 1

Offset

1,2

Links

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

Formula

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

T(n, 1) = A076078(n).

T(n, k) = A338507(n, A000005(n)+1-k) for k = 1..A000005(n)-1.

T(n, A000005(n)) = 1.

Example

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

Mathematica

Array[Tally[Map[GCD @@ # &, Rest[Subsets@ Divisors[#]]]][[All, -1]] &, 24] // Flatten (* Michael De Vlieger, Nov 04 2020 *)

Prog

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

Crossrefs

Cf. A000005, A076078, A100587, A338507 (LCM variant).

Sequence in context: A068341 A360738 A321368 * A100380 A205403 A080825

Adjacent sequences: A338505 A338506 A338507 * A338509 A338510 A338511

Keyword

nonn,tabf

Author

Rémy Sigrist, Oct 31 2020

Status

approved