A190471 Numbers with prime factorization p^2*q^4*r^4 where p, q, and r are distinct primes.

32400, 63504, 90000, 156816, 202500, 219024, 345744, 374544, 467856, 490000, 685584, 777924, 960400, 1089936, 1210000, 1245456, 1690000, 1774224, 2108304, 2178576, 2396304, 2480625, 2862864, 2890000, 3610000, 3640464, 4112784, 4511376

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(4)^2/2 - P(2)*P(8)/2 - P(4)*P(6) + P(10) = 0.00010139253539568059065..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 4, 4}; Select[Range[3500000], f] (*and*) lst={}; Do[If[k!=n && k!=m && n!=m, AppendTo[lst, Prime[k]^2*Prime[n]^4*Prime[m]^4]], {n, 33}, {m, 33}, {k, 33}]; Take[Union@lst, 60]

Prog

(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\4)^(1/8), t1=p^4; forprime(q=p+1, (lim\t1)^(1/4), t2=t1*q^4; forprime(r=2, sqrt(lim\t2), if(p==r||q==r, next); listput(v, t2*r^2)))); Set(v) \\ Charles R Greathouse IV, Aug 25 2016

Crossrefs

Cf. A190469, A190470.

Cf. A085548, A085964, A085966, A085968.

Sequence in context: A156038 A156048 A234224 * A236994 A156421 A156423

Adjacent sequences: A190468 A190469 A190470 * A190472 A190473 A190474

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 10 2011

Status

approved