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A190377
Numbers with prime factorization p^2*q^2*r^2*s^2 where p, q, r, and s are distinct primes.
1
44100, 108900, 152100, 213444, 260100, 298116, 324900, 476100, 509796, 592900, 636804, 736164, 756900, 828100, 864900, 933156, 1232100, 1258884, 1334025, 1416100, 1483524, 1512900, 1572516, 1664100, 1695204, 1758276, 1768900, 1863225
OFFSET
1,1
FORMULA
Sum_{n>=1} 1/a(n) = (P(2)^4 - 6*P(2)^2*P(4) + 8*P(2)*P(6) + 3*P(4)^2 - 6*P(8))/24 = 0.00010511750849230980748..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024
MATHEMATICA
f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 2, 2, 2}; Select[Range[3000000], f]
PROG
(PARI) list(lim)=my(v=List(), t1, t2, t3); forprime(p=2, sqrtint(lim\900), t1=p^2; forprime(q=2, sqrtint(lim\(36*t1)), if(q==p, next); t2=q^2*t1; forprime(r=2, sqrtint(lim\(4*t2)), if(r==p || r==q, next); t3=r^2*t2; forprime(s=2, sqrtint(lim\t3), if(s==p || s==q || s==r, next); listput(v, t3*s^2))))); Set(v) \\ Charles R Greathouse IV, Aug 25 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved