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A121382 Number of ways of writing n as x*y*z, with x <= y <= z and gcd(x,y) = gcd(y,z) = 1. 2
1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 2, 1, 5, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 5, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 7, 1, 2, 2, 1, 2, 5, 1, 2, 2, 5, 1, 2, 1, 2, 2, 2, 2, 5, 1, 3, 1, 2, 1, 6, 2, 2, 2, 2, 1, 6, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 5, 1, 2, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
3-factor analog of A007875 (number of ways of writing n as x*y, with x <= y and gcd(x,y)=1).
a(n) = 1 iff n is a prime power (A000961).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000 (first 2048 terms from Antti Karttunen)
EXAMPLE
a(4) = 1 because 4 = 1*1*4.
a(6) = 2 because 6 = 1*1*6 = 1*2*3.
a(24) = 3 because 24 = 1*1*24 = 1*3*8 = 2*3*4.
a(30) = 5 because 30 = 1*1*30 = 1*2*15 = 1*3*10 = 1*5*6 = 2*3*5.
MAPLE
N:= 1000:
A:= Vector(N):
for y from 1 to floor(sqrt(N)) do
X:= select(t -> igcd(t, y)=1, [$1..y]);
Z:= select(t -> igcd(t, y)=1, [$y..N/y]);
for x in X do
for z in Z while x*y*z <= N do
A[x*y*z]:= A[x*y*z]+1
od od:
od:
convert(A, list); # Robert Israel, Aug 27 2017
MATHEMATICA
f[n_] := Block[{d = Divisors@n, m = DivisorSigma[0, n], s = {}}, If[m == 2, 1, Do[ AppendTo[s, {d[[p]], d[[q]], d[[r]]}], {r, m}, {q, r}, {p, q}]; Length@ Select[s, Times @@ # == n && GCD[ #[[1]], #[[2]]] == GCD[ #[[2]], #[[3]]] == 1 &]]]; Array[f, 105] (* Robert G. Wilson v, Sep 11 2006 *)
PROG
(PARI) A121382(n) = { my(s=0); fordiv(n, x, for(y=x, n, for(z=y, n, if((x*y*z==n)&&(1==gcd(x, y))&&(1==gcd(y, z)), s++)))); (s); }; \\ Antti Karttunen, Aug 27 2017
CROSSREFS
First occurrence of k: A122829.
Sequence in context: A333175 A294893 A336570 * A305150 A351202 A333145
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Sep 06 2006
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Sep 11 2006
Name clarified by Antti Karttunen, Aug 27 2017
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)