A123074 Number of ordered triples of primes (p,q,r) such that pqr = n.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 1, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 3, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 6, 0, 3, 0, 6, 0, 0, 0, 0, 3, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 3, 0, 0, 6, 0, 0, 6

Offset: 1

Author

N. J. A. Sloane and T. D. Noe, Sep 29 2006

Keywords

• nonn

Comments

For distinct primes p, q and r, a(p^3) = 1, a(p^2 q) = 3, a(pqr) = 6, otherwise (when A101605(n) = 0), a(n) = 0. - Comment clarified by David A. Corneth and Antti Karttunen, Jul 23 2017

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A001221, A001222, A101605, A123073, A014612.

Programs

Mathematica

Join[{0}, Table[e=Sort[Transpose[FactorInteger[n]][[2]]]; Which[e=={3}, 1, e=={1,2}, 3, e=={1,1,1}, 6, True, 0], {n,2,150}]] (* T. D. Noe, Sep 29 2006 *)

PARI

A123074(n) = if(3==bigomega(n),binomial(1+omega(n),2),0); \\ Antti Karttunen, Jul 23 2017

Python

from sympy import factorint
def A123074(n): return (1,3,6)[len(f)-1] if sum(f:=factorint(n).values())==3 else 0 # Chai Wah Wu, Oct 20 2024

Extensions

More terms from T. D. Noe, Sep 29 2006