A190465 Numbers with prime factorization p^5q^5.

7776, 100000, 537824, 759375, 4084101, 5153632, 11881376, 39135393, 45435424, 52521875, 79235168, 90224199, 205962976, 345025251, 503284375, 601692057, 656356768, 916132832, 1160290625, 1564031349, 2219006624, 2706784157, 3707398432

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 10 2011

Keywords

• nonn

Links

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

Crossrefs

Cf. A179699, A179705, A190464.

Cf. A085965.

Programs

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1}; Select[Range[10000],f]^5

PARI

list(lim)=my(v=List(),t);forprime(p=2, lim^(1/10), t=p^5;forprime(q=p+1, (lim\t)^(1/5), listput(v,t*q^5))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011

Formula

Sum_{n>=1} 1/a(n) = (P(5)^2 - P(10))/2 = (A085965^2 - P(10))/2 = 0.000142..., where P is the prime zeta function. - Amiram Eldar, Jul 06 2020