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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

Table of n, a(n) for n=1..81.

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.)