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 A190471 Numbers with prime factorization p^2*q^4*r^4 where p, q, and r are distinct primes. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 11 20:46 EDT 2024. Contains 375073 sequences. (Running on oeis4.)