A190472 Numbers with prime factorization p^3*q^3*r^4 where p, q, and r are distinct primes.

54000, 81000, 135000, 148176, 222264, 518616, 574992, 686000, 862488, 949104, 1423656, 1715000, 2122416, 2401000, 2662000, 2963088, 3162456, 3183624, 3472875, 4394000, 4444632, 5256144, 5788125, 6169176, 6655000, 7304528, 7884216

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Will Nicholes, List of prime signatures, 2010.

Index to sequences related to prime signature.

Formula

Sum_{n>=1} 1/a(n) = P(3)^2*P(4)/2 - P(4)*P(6)/2 - P(3)*P(7) + P(10) = 0.000064520760706206924448..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={3, 3, 4}; Select[Range[5000000], f] (*and*) lst={}; Do[If[k!=n && k!=m && n!=m, AppendTo[lst, Prime[k]^3*Prime[n]^3*Prime[m]^4]], {n, 25}, {m, 25}, {k, 25}]; Take[Union@lst, 60]

Prog

(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\216)^(1/4), t1=p^4; forprime(q=2, (lim\t1)^(1/3), if(p==q, next); t2=t1*q^3; forprime(r=q+1, (lim\t2)^(1/3), if(p==r, next); listput(v, t2*r^3)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 24 2011

Crossrefs

Cf. A190470, A190471.

Cf. A085541, A085964, A085966, A085967.

Sequence in context: A164720 A151959 A164724 * A038564 A243362 A224624

Adjacent sequences: A190469 A190470 A190471 * A190473 A190474 A190475

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 10 2011

Status

approved