A190469 Numbers with prime factorization p^2*q^2*r^6 where p, q, and r are distinct primes.

14400, 28224, 69696, 72900, 78400, 97344, 142884, 166464, 193600, 207936, 270400, 304704, 352836, 379456, 462400, 484416, 492804, 529984, 553536, 562500, 577600, 788544, 842724, 846400, 893025, 906304, 968256, 1052676, 1065024, 1132096

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)^2*P(6)/2 - P(2)*P(8)/2 - P(4)*P(6)/2 - P(2)*P(8) + P(10) = 0.00024535673248061231753..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 2, 6}; Select[Range[1600000], f]

Prog

(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\36)^(1/6), t1=p^6; forprime(q=2, sqrt(lim\t1), if(p==q, next); t2=t1*q^2; forprime(r=q+1, sqrt(lim\t2), if(p==r, next); listput(v, t2*r^2)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011

Crossrefs

Cf. A190466, A190467, A190468.

Cf. A085548, A085964, A085966, A085968.

Sequence in context: A237788 A106725 A253266 * A237372 A250851 A226286

Adjacent sequences: A190466 A190467 A190468 * A190470 A190471 A190472

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 10 2011

Status

approved