A122179 - OEIS

%I #10 Nov 08 2018 07:42:11

%S 0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,2,0,0,1,1,0,1,0,2,0,0,

%T 0,3,0,0,0,2,0,1,0,1,1,0,0,4,0,1,0,1,0,2,0,2,0,0,0,4,0,0,1,3,0,1,0,1,

%U 0,1,0,6,0,0,1,1,0,1,0,4,1,0,0,4,0,0,0,2,0,4,0,1,0,0,0,6,0,1,1,3,0,1,0,2,1

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

%C x,y,z are proper factors of n. a(n) > 0 iff n is a term of A033942; a(n) = 0 iff n is a term of A037143.

%H Seiichi Manyama, <a href="/A122179/b122179.txt">Table of n, a(n) for n = 1..8192</a> (terms 1..2048 from Antti Karttunen)

%e a(24) = 2 because 24 = 2*2*6 = 2*3*4, two products of three proper factors of 24.

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

%o (PARI) A122179(n) = { my(s=0); fordiv(n, x, if((x>1)&&(x<n),for(y=x, n-1, for(z=y, n-1, if(x*y*z==n, s++))))); (s); }; \\ _Antti Karttunen_, Aug 24 2017

%Y Cf. A034836, A033942, A037143, A088432, A088433, A088434, A122180.

%K nonn

%O 1,24

%A _Rick L. Shepherd_, Aug 23 2006