A190382 Numbers with prime factorization p^2*q^2*r^2*s^3 where p, q, r, and s are distinct primes.

88200, 132300, 217800, 220500, 304200, 308700, 326700, 426888, 456300, 520200, 544500, 596232, 640332, 649800, 760500, 780300, 894348, 952200, 974700, 1019592, 1185800, 1197900, 1273608, 1300500, 1428300, 1472328, 1494108, 1513800

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)^3*P(3) - 3*P(2)^2*P(5) - 3*P(2)*P(3)*P(4) + 6*P(2)*P(7) + 2*P(3)*P(6) + 3*P(4)*P(5) - 6*P(9))/6 = 0.00010783911499432484110..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 2, 2, 3}; Select[Range[2000000], f]

Prog

(PARI) list(lim)=my(v=List(), t1, t2, t3); forprime(p=2, sqrtnint(lim\900, 3), t1=p^3; forprime(q=2, sqrtint(lim\(36*t1)), if(q==p, next); t2=q^2*t1; forprime(r=2, sqrtint(lim\(4*t2)), if(r==p || r==q, next); t3=r^2*t2; forprime(s=2, sqrtint(lim\t3), if(s==p || s==q || s==r, next); listput(v, t3*s^2))))); Set(v) \\ Charles R Greathouse IV, Aug 25 2016

Crossrefs

Cf. A190319, A190320.

Cf. A085548, A085541, A085964, A085965, A085966, A085967, A085969.

Sequence in context: A234442 A204508 A180106 * A068536 A183728 A237908

Adjacent sequences: A190379 A190380 A190381 * A190383 A190384 A190385

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 09 2011

Status

approved