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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,18 LINKS 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. Cf. A007562, A007716, A014963, A045778, A050370, A162247, A289509, A303386, A303546. Cf. A317752, A317755, A317757. Sequence in context: A214157 A246720 A246690 * A090465 A052344 A147768 Adjacent sequences:  A317745 A317746 A317747 * A317749 A317750 A317751 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Aug 06 2018 STATUS approved

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Last modified September 21 13:00 EDT 2020. Contains 337272 sequences. (Running on oeis4.)