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 A277130 Number of planar branching factorizations of n. 6
 0, 1, 1, 2, 1, 3, 1, 6, 2, 3, 1, 14, 1, 3, 3, 24, 1, 14, 1, 14, 3, 3, 1, 78, 2, 3, 6, 14, 1, 25, 1, 112, 3, 3, 3, 110, 1, 3, 3, 78, 1, 25, 1, 14, 14, 3, 1, 464, 2, 14, 3, 14, 1, 78, 3, 78, 3, 3, 1, 206, 1, 3, 14, 568, 3, 25, 1, 14, 3, 25, 1, 850, 1, 3, 14, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A planar branching factorization of n is either the number n itself or a sequence of at least two planar branching factorizations, one of each factor in an ordered factorization of n. - Gus Wiseman, Sep 11 2018 LINKS Daniel Mondot, Table of n, a(n) for n = 1..9999 A. Knopfmacher, M. E. Mays, A survey of factorization counting functions, International Journal of Number Theory, 1(4):563-581,(2005). See page 15. FORMULA a(prime^n) = A118376(n). a(product of n distinct primes) = A319122(n). - Gus Wiseman, Sep 11 2018 EXAMPLE From Gus Wiseman, Sep 11 2018: (Start) The a(12) = 14 planar branching factorizations:   12,   (2*6), (3*4), (4*3), (6*2), (2*2*3), (2*3*2), (3*2*2),   (2*(2*3)), (2*(3*2)), (3*(2*2)), ((2*2)*3), ((2*3)*2), ((3*2)*2). (End) MATHEMATICA ordfacs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@ordfacs[n/d], {d, Rest[Divisors[n]]}]] otfs[n_]:=Prepend[Join@@Table[Tuples[otfs/@f], {f, Select[ordfacs[n], Length[#]>1&]}], n]; Table[Length[otfs[n]], {n, 20}] (* Gus Wiseman, Sep 11 2018 *) PROG (C) #include #include #include #define MAX 10000 /* Number of planar branching factorizations of n. */ #define lu unsigned long lu nbr[MAX]; /* number of branching */ lu a, b, d, e; /* temporary variables */ lu n; lu m, p; // factors of n lu x; // square root of n void main(unsigned argc, char *argv[]) {   memset(nbr, 0, MAX*sizeof(lu));   for (b=0, n=1; n

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Last modified September 18 18:19 EDT 2021. Contains 347533 sequences. (Running on oeis4.)