A179699 Numbers of the form p^8*q^2 where p and q are distinct primes.

2304, 6400, 12544, 26244, 30976, 43264, 73984, 92416, 135424, 164025, 215296, 246016, 321489, 350464, 430336, 473344, 565504, 719104, 793881, 891136, 952576, 1108809, 1149184, 1290496, 1364224, 1562500, 1597696, 1763584

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 24 2010

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Will Nicholes, Prime Signatures

Crossrefs

Cf. A085548, A085968.

Programs

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={2,8}; Select[Range[10^6], f]

PARI

list(lim)=my(v=List(),t);forprime(p=2, (lim\4)^(1/8), t=p^8;forprime(q=2, sqrt(lim\t), if(p==q, next);listput(v,t*q^2))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 24 2011

Formula

Sum_{n>=1} 1/a(n) = P(2)*P(8) - P(10) = A085548 * A085968 - P(10) = 0.000843..., where P is the prime zeta function. - Amiram Eldar, Jul 06 2020