A190115 Numbers with prime factorization p^2*q^3*r^4 where p, q, and r are distinct primes.

10800, 16200, 18000, 21168, 31752, 40500, 45000, 49392, 52272, 67500, 73008, 78408, 98000, 109512, 111132, 124848, 137200, 155952, 172872, 187272, 191664, 228528, 233928, 242000, 245000, 259308, 316368, 338000, 342792, 363312, 415152

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(4) - P(2)*P(7) - P(3)*P(6) - P(4)*P(5) + 2*P(9) = 0.00061171477910848082277..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 3, 4}; Select[Range[900000], f]

Prog

(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\72)^(1/4), t1=p^4; 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. A093770, A190012, A190014.

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

Sequence in context: A216142 A340303 A093770 * A203394 A144716 A123078

Adjacent sequences: A190112 A190113 A190114 * A190116 A190117 A190118

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 04 2011

Status

approved