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 A319300 Irregular triangle where T(n,k) is the number of strict integer partitions of n with GCD equal to the k-th divisor of n. 2
 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 2, 1, 0, 1, 4, 1, 4, 1, 0, 1, 6, 1, 1, 7, 2, 0, 1, 11, 1, 10, 2, 1, 1, 0, 1, 17, 1, 17, 4, 0, 1, 23, 2, 1, 1, 26, 4, 1, 0, 1, 37, 1, 36, 6, 2, 1, 0, 1, 53, 1, 53, 7, 2, 1, 0, 1, 70, 4, 1, 1, 77, 11, 0, 1, 103, 1, 103, 10, 4, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 LINKS FORMULA T(n,k) = A078374(n/A027750(n,k)). EXAMPLE Triangle begins:    1    0  1    1  1    1  0  1    2  1    2  1  0  1    4  1    4  1  0  1    6  1  1    7  2  0  1   11  1   10  2  1  1  0  1   17  1   17  4  0  1   23  2  1  1   26  4  1  0  1   37  1   36  6  2  1  0  1   53  1   53  7  2  1  0  1 MATHEMATICA Table[Length[Select[IntegerPartitions[n], And[UnsameQ@@#, GCD@@#==k]&]], {n, 20}, {k, Divisors[n]}] CROSSREFS A regular version is A303138. Row lengths are A000005. Row sums are A000009. First column is A078374. Cf. A000837, A027750, A289508, A289509, A303140, A303280, A319299, A319301. Sequence in context: A272677 A165579 A130911 * A118829 A118832 A122807 Adjacent sequences:  A319297 A319298 A319299 * A319301 A319302 A319303 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Sep 16 2018 STATUS approved

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Last modified October 14 17:27 EDT 2019. Contains 328022 sequences. (Running on oeis4.)