A190470 Numbers with prime factorization p^2*q^3*r^5 where p, q, and r are distinct primes.

21600, 36000, 42336, 48600, 95256, 98784, 104544, 121500, 146016, 196000, 225000, 235224, 249696, 274400, 311904, 328536, 333396, 337500, 383328, 457056, 484000, 561816, 632736, 676000, 701784, 726624, 830304, 1028376, 1064800, 1156000

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(2)*P(3)*P(5) - P(2)*P(8) - P(3)*P(7) - P(5)^2 + 2*P(10) = 0.00025025315357155375895..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 3, 5}; Select[Range[2500000], f] (*and*) lst={}; Do[If[k!=n && k!=m && n!=m, AppendTo[lst, Prime[k]^2*Prime[n]^3*Prime[m]^5]], {n, 20}, {m, 20}, {k, 20}]; Take[Union@lst, 60]

Prog

(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\72)^(1/5), t1=p^5; forprime(q=2, (lim\t1)^(1/3), if(p==q, next); t2=t1*q^3; forprime(r=2, sqrt(lim\t2), if(p==r||q==r, next); listput(v, t2*r^2)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 24 2011

Crossrefs

Cf. A190467, A190468, A190469.

Cf. A085548, A085541, A085965, A085967, A085968.

Sequence in context: A252393 A211236 A221002 * A113620 A074812 A037160

Adjacent sequences: A190467 A190468 A190469 * A190471 A190472 A190473

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 10 2011

Status

approved