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A317748
Irregular triangle where T(n,d) is the number of factorizations of n into factors > 1 with GCD d.
8
0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 3, 1, 0, 1, 0, 1, 2, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 3, 3, 0, 0, 0, 0, 0, 1, 0, 1, 1
OFFSET
1,18
EXAMPLE
Triangle begins:
1: 0
2: 0 1
3: 0 1
4: 0 1 1
5: 0 1
6: 1 0 0 1
7: 0 1
8: 0 2 0 1
9: 0 1 1
10: 1 0 0 1
11: 0 1
12: 2 1 0 0 0 1
13: 0 1
14: 1 0 0 1
15: 1 0 0 1
16: 0 3 1 0 1
17: 0 1
18: 2 0 1 0 0 1
19: 0 1
20: 2 1 0 0 0 1
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
goc[n_, m_]:=Length[Select[facs[n], And[And@@(Divisible[#, m]&/@#), GCD@@(#/m)==1]&]];
Table[goc[n, d], {n, 30}, {d, Divisors[n]}]
CROSSREFS
Row lengths are A000005. Row sums are A001055. First column is A281116. Number of nonzero terms in each row is A317751.
Sequence in context: A246720 A343030 A246690 * A090465 A364357 A052344
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Aug 06 2018
STATUS
approved