The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Cf. A000040, A001248, A001358, A007304, A007875, A030078. First occurrence of k: A122829. Sequence in context: A333175 A294893 A336570 * A305150 A333145 A335449 Adjacent sequences:  A121379 A121380 A121381 * A121383 A121384 A121385 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)