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A088432
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Number of ways to write n as n = u*v*w with 1 <= u < v <= w.
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6
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0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 3, 0, 2, 1, 1, 0, 4, 1, 1, 1, 2, 0, 4, 0, 3, 1, 1, 1, 5, 0, 1, 1, 4, 0, 4, 0, 2, 2, 1, 0, 7, 1, 3, 1, 2, 0, 4, 1, 4, 1, 1, 0, 8, 0, 1, 2, 4, 1, 4, 0, 2, 1, 4, 0, 9, 0, 1, 3, 2, 1, 4, 0, 6, 2, 1, 0, 8, 1, 1, 1, 4, 0, 8, 1, 2, 1, 1, 1, 9, 0, 3, 2, 6, 0, 4, 0, 4, 4, 1, 0, 9, 0, 4, 1, 6, 0, 4, 1, 2, 2, 1, 1, 14
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OFFSET
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1,12
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LINKS
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FORMULA
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EXAMPLE
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n=12: (1,2,6), (1,3,4): therefore a(12)=2;
n=18: (1,2,9), (1,3,6), (2,3,3): therefore a(18)=3.
For n = p*q, p < q primes: n = 1 * p * q, so a(n) = 1.
For n = p^2, p prime: n = 1 * p * p, so a(n) = 1.
For n = p^3, p prime: n = 1 * p * p^2, so a(n) = 1.
For n = p*q^2, p < q < p^2: n = 1 * p * pq = 1* q * p^2, so a(n) = 2 (see n=12).
For n = p*q^2, p < p^2 < q: n = 1 * p * pq = 1 * p^2 * q, so a(n) = 2
For n = p^4, p prime: n = 1 * p * p^3 = 1 * p^2 * p^2, so a(n) = 2.
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MATHEMATICA
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a[n_] := Module[{s = 0}, Do[Do[Do[If[u v w == n, s++], {w, v, n}], {v, u + 1, n - 1}], {u, Divisors[n]}]; s];
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PROG
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(PARI) A088432(n) = { my(s=0); fordiv(n, u, for(v=u+1, n-1, for(w=v, n, if(u*v*w==n, s++)))); (s); }; \\ Antti Karttunen, Aug 24 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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