A338508 - OEIS

%I #11 Nov 08 2020 12:34:53

%S 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,

%T 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,

%U 4,2,1,10,2,2,1,10,2,2,1,2,1,184,44,8,10,4,2,2,1

%N 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.

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

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

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

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

%e Triangle begins:

%e      1: [1]

%e      2: [2, 1]

%e      3: [2, 1]

%e      4: [4, 2, 1]

%e      5: [2, 1]

%e      6: [10, 2, 2, 1]

%e      7: [2, 1]

%e      8: [8, 4, 2, 1]

%e      9: [4, 2, 1]

%e     10: [10, 2, 2, 1]

%e     11: [2, 1]

%e     12: [44, 10, 4, 2, 2, 1]

%e     13: [2, 1]

%e     14: [10, 2, 2, 1]

%e     15: [10, 2, 2, 1]

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

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

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

%K nonn,tabf

%O 1,2

%A _Rémy Sigrist_, Oct 31 2020