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
Examples
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]
Programs
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Mathematica
Array[Tally[Map[GCD @@ # &, Rest[Subsets@ Divisors[#]]]][[All, -1]] &, 24] // Flatten (* Michael De Vlieger, Nov 04 2020 *)
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PARI
row(n) = { my (d=divisors(n), r=vector(#d)); for (m=1, 2^#d-1, r[setsearch(d, gcd(vecextract(d, m)))]++); r }