cp's OEIS Frontend

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.

%I A338508 #11 Nov 08 2020 12:34:53
%S A338508 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 A338508 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 A338508 4,2,1,10,2,2,1,10,2,2,1,2,1,184,44,8,10,4,2,2,1
%N 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.
%F A338508 Sum_{k = 1..A000005(n)} T(n, k) = A100587(n).
%F A338508 T(n, 1) = A076078(n).
%F A338508 T(n, k) = A338507(n, A000005(n)+1-k) for k = 1..A000005(n)-1.
%F A338508 T(n, A000005(n)) = 1.
%e A338508 Triangle begins:
%e A338508      1: [1]
%e A338508      2: [2, 1]
%e A338508      3: [2, 1]
%e A338508      4: [4, 2, 1]
%e A338508      5: [2, 1]
%e A338508      6: [10, 2, 2, 1]
%e A338508      7: [2, 1]
%e A338508      8: [8, 4, 2, 1]
%e A338508      9: [4, 2, 1]
%e A338508     10: [10, 2, 2, 1]
%e A338508     11: [2, 1]
%e A338508     12: [44, 10, 4, 2, 2, 1]
%e A338508     13: [2, 1]
%e A338508     14: [10, 2, 2, 1]
%e A338508     15: [10, 2, 2, 1]
%t A338508 Array[Tally[Map[GCD @@ # &, Rest[Subsets@ Divisors[#]]]][[All, -1]] &, 24] // Flatten (* _Michael De Vlieger_, Nov 04 2020 *)
%o A338508 (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 A338508 Cf. A000005, A076078, A100587, A338507 (LCM variant).
%K A338508 nonn,tabf
%O A338508 1,2
%A A338508 _Rémy Sigrist_, Oct 31 2020