A216426 Numbers of the form a^2*b^3, where a != b and a, b > 1.

72, 108, 128, 200, 256, 288, 392, 432, 500, 512, 576, 648, 675, 800, 864, 968, 972, 1125, 1152, 1323, 1352, 1372, 1568, 1600, 1728, 1800, 1944, 2000, 2048, 2187, 2304, 2312, 2592, 2700, 2888, 2916, 3087, 3136, 3200, 3267, 3456, 3528, 3872, 3888, 4000

Offset

1,1

Comments

Terms of A216427 that are not 5th powers of squarefree numbers (A113850) and not 10th powers of primes (A030629). - Amiram Eldar, Feb 07 2023

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

Sum_{n>=1} 1/a(n) = 2 + ((zeta(2)-1)*(zeta(3)-1)-1)/zeta(6) - zeta(5)/zeta(10) - P(6) - P(10) = 0.09117811499514578262..., where P(s) is the prime zeta function. - Amiram Eldar, Feb 07 2023

Mathematica

With[{upto=4000}, Select[Union[Flatten[{#[[1]]^2 #[[2]]^3, #[[2]]^2 #[[1]]^3}& /@ Subsets[Range[2, Surd[upto, 2]], {2}]]], #<=upto&]](* Harvey P. Dale, Jan 04 2014 *)
pMx = 25; mx = 2^3 pMx^2; t = Flatten[Table[If[a != b, a^2 b^3, 0], {a, 2, mx^(1/2)}, {b, 2, mx^(1/3)}]]; Union[Select[t, 0 < # <= mx &]] (* T. D. Noe, Jan 02 2014 *)

Prog

(PARI) list(lim)=my(v=List()); for(b=2, sqrtnint(lim\4, 3), for(a=2, sqrtint(lim\b^3), if(a!=b, listput(v, a^2*b^3)))); Set(v) \\ Charles R Greathouse IV, Jan 02 2014

Crossrefs

Cf. A143610.

Subsequence of A216427. - Zak Seidov, Jan 03 2014

Cf. A002117, A013661, A013663, A013664, A013668, A030629, A085966, A113850.

Sequence in context: A258695 A102562 A357460 * A308053 A356871 A359280

Adjacent sequences: A216423 A216424 A216425 * A216427 A216428 A216429

Keyword

nonn

Author

V. Raman, Sep 07 2012

Extensions

Name corrected by Charles R Greathouse IV, Jan 02 2014

Status

approved