A122179 Number of ways to write n as n = x*y*z with 1<x<=y<=z<n.

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, 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, 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

Offset

1,24

Comments

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.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..8192 (terms 1..2048 from Antti Karttunen)

Example

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

Prog

(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, ", "))
(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

Crossrefs

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

Sequence in context: A125005 A309367 A347709 * A335877 A125203 A023565

Adjacent sequences: A122176 A122177 A122178 * A122180 A122181 A122182

Keyword

nonn

Author

Rick L. Shepherd, Aug 23 2006

Status

approved