A179646 Product of the 5th power of a prime and different distinct prime of the 2nd power (p^5*q^2).

288, 800, 972, 1568, 3872, 5408, 6075, 9248, 11552, 11907, 12500, 16928, 26912, 28125, 29403, 30752, 41067, 43808, 53792, 59168, 67228, 70227, 70688, 87723, 89888, 111392, 119072, 128547, 143648, 151263, 153125, 161312, 170528, 199712

Offset

1,1

Comments

288=2^5*3^2, 800=2^5*5^2,..

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Will Nicholes, Prime Signatures

Index to sequences related to prime signature

Formula

Sum_{n>=1} 1/a(n) = P(2)*P(5) - P(7) = A085548 * A085965 - A085967 = 0.007886..., where P is the prime zeta function. - Amiram Eldar, Jul 06 2020

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 5}; Select[Range[200000], f]

Prog

(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\4)^(1/5), t=p^5; forprime(q=2, sqrt(lim\t), if(p==q, next); listput(v, t*q^2))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011

Crossrefs

Cf. A030636, A046308, A007774.

Cf. A085548, A085965, A085967.

Sequence in context: A158253 A292054 A250788 * A281236 A237369 A280936

Adjacent sequences: A179643 A179644 A179645 * A179647 A179648 A179649

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2010

Status

approved