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A190472
Numbers with prime factorization p^3*q^3*r^4 where p, q, and r are distinct primes.
5
54000, 81000, 135000, 148176, 222264, 518616, 574992, 686000, 862488, 949104, 1423656, 1715000, 2122416, 2401000, 2662000, 2963088, 3162456, 3183624, 3472875, 4394000, 4444632, 5256144, 5788125, 6169176, 6655000, 7304528, 7884216
OFFSET
1,1
FORMULA
Sum_{n>=1} 1/a(n) = P(3)^2*P(4)/2 - P(4)*P(6)/2 - P(3)*P(7) + P(10) = 0.000064520760706206924448..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024
MATHEMATICA
f[n_]:=Sort[Last/@FactorInteger[n]]=={3, 3, 4}; Select[Range[5000000], f] (*and*) lst={}; Do[If[k!=n && k!=m && n!=m, AppendTo[lst, Prime[k]^3*Prime[n]^3*Prime[m]^4]], {n, 25}, {m, 25}, {k, 25}]; Take[Union@lst, 60]
PROG
(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\216)^(1/4), t1=p^4; forprime(q=2, (lim\t1)^(1/3), if(p==q, next); t2=t1*q^3; forprime(r=q+1, (lim\t2)^(1/3), if(p==r, next); listput(v, t2*r^3)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 24 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved