OFFSET
1,48
COMMENTS
x,y,z are distinct proper factors of n. See A122181 for n such that a(n) > 0.
If n has at most five divisors then a(n) = 0. - David A. Corneth, Oct 24 2024
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1001 terms from Antti Karttunen)
FORMULA
a(n) = A200214(n)/6. - Antti Karttunen, Jul 08 2017
EXAMPLE
a(48) = 2 because 48 = 2*3*8 = 2*4*6, two products of three distinct proper factors of 48.
PROG
(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, ", "))
(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
(PARI) a(n) = {
my(d = divisors(n));
if(#d <= 5, return(0));
my(res = 0, q);
for(i = 2, #d,
q = d[#d + 1 - i];
if(d[i]^2 > q,
return(res)
);
for(j = i + 1, #d,
qj = q/d[j];
if(qj <= d[j],
next(2)
);
if(denominator(qj) == 1 && n % qj == 0,
res++
);
);
);
res
} \\ David A. Corneth, Oct 24 2024
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Rick L. Shepherd, Aug 23 2006
STATUS
approved