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A122180 Number of ways to write n as n = x*y*z with 1 < x < y < z < n. 7

%I

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,

%T 0,1,0,0,0,1,0,1,0,0,0,0,0,2,0,0,0,0,0,1,0,1,0,0,0,3,0,0,0,1,0,1,0,0,

%U 0,1,0,3,0,0,0,0,0,1,0,2,0,0,0,3,0,0,0,1,0,3,0,0,0,0,0,4,0,0,0,1,0,1,0,1,1

%N Number of ways to write n as n = x*y*z with 1 < x < y < z < n.

%C x,y,z are distinct proper factors of n. See A122181 for n such that a(n) > 0.

%H Antti Karttunen, <a href="/A122180/b122180.txt">Table of n, a(n) for n = 1..1001</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = A200214(n)/6. - _Antti Karttunen_, Jul 08 2017

%e a(48) = 2 because 48 = 2*3*8 = 2*4*6, two products of three distinct proper factors of 48.

%o (PARI) for(n=1,105, t=0; for(x=2,n-1, for(y=x+1,n-1, for(z=y+1,n-1, if(x*y*z==n, t++)))); print1(t,", "))

%o (PARI) A122180(n) = { my(s=0); fordiv(n, x, if((x>1)&&(x<n),for(y=x+1, n-1, for(z=y+1, n-1, if(x*y*z==n, s++))))); (s); }; \\ Just slightly optimized from the above. - _Antti Karttunen_, Jul 08 2017

%Y Cf. A034836, A088432, A088433, A088434, A122179, A122181, A200214.

%K nonn

%O 1,48

%A _Rick L. Shepherd_, Aug 23 2006

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Last modified April 23 09:35 EDT 2019. Contains 322385 sequences. (Running on oeis4.)