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

1,12

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A360016 A035678 A094518 * A095269 A356302 A308275

Adjacent sequences: A123071 A123072 A123073 * A123075 A123076 A123077

Keyword

nonn

Author

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

Extensions

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

Status

approved