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A338508
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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.
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1
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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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]
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MATHEMATICA
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Array[Tally[Map[GCD @@ # &, Rest[Subsets@ Divisors[#]]]][[All, -1]] &, 24] // Flatten (* Michael De Vlieger, Nov 04 2020 *)
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PROG
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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 }
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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