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 A281116 Number of factorizations of n>=2 into factors greater than 1 with no common divisor other than 1 (a(1)=0 by convention). 105
 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 0, 2, 0, 4, 0, 0, 1, 1, 1, 5, 0, 1, 1, 3, 0, 4, 0, 2, 2, 1, 0, 5, 0, 2, 1, 2, 0, 3, 1, 3, 1, 1, 0, 8, 0, 1, 2, 0, 1, 4, 0, 2, 1, 4, 0, 9, 0, 1, 2, 2, 1, 4, 0, 5, 0, 1, 0, 8, 1, 1, 1, 3, 0, 8, 1, 2, 1, 1, 1, 7, 0, 2, 2, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS Let (e1, e2, ..., ek) be a prime-signature of n (that is, n = p^e1 * q^e2 * ... * r^ek for some primes, p, q, ..., r). Then a(n) is the number of ways of partitioning multiset {e1 x 1, e2 x 2, ..., ek x k} into multisets such that none of the numbers 1 .. k is present in all member multisets of that set partition. - Antti Karttunen, Sep 08 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 EXAMPLE a(6)=1:  (2*3) a(12)=2; (2*2*3)       (3*4) a(24)=3: (2*2*2*3)     (2*3*4)     (3*8) a(30)=4: (2*3*5)       (2*15)      (3*10)    (5*6) a(36)=5: (2*2*3*3)     (2*2*9)     (2*3*6)   (3*3*4)   (4*9) a(96)=7: (2*2*2*2*2*3) (2*2*2*3*4) (2*2*3*8) (2*3*4*4) (2*3*16) (3*4*8) (3*32). MATHEMATICA postfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[postfacs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Length[Select[postfacs[n], GCD@@#===1&]], {n, 2, 100}] PROG (PARI) A281116(n, m=n, facs=List([])) = if(1==n, (1==gcd(Vec(facs))), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs, d); s += A281116(n/d, d, newfacs))); (s)); \\ Antti Karttunen, Sep 08 2018 CROSSREFS Cf. A001055, A007916, A089233, A162247, A259936, A281113, A317751. First column of A317748. Sequence in context: A236441 A327695 A319058 * A089233 A066620 A219023 Adjacent sequences:  A281113 A281114 A281115 * A281117 A281118 A281119 KEYWORD nonn AUTHOR Gus Wiseman, Jan 15 2017 EXTENSIONS Term a(1) = 0 prepended by Antti Karttunen, Sep 08 2018 STATUS approved

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Last modified June 7 04:32 EDT 2020. Contains 334836 sequences. (Running on oeis4.)