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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
OFFSET
1,9
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.
Sequence in context: A367739 A165579 A130911 * A118829 A118832 A122807
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Sep 16 2018
STATUS
approved