|
%I #22 Feb 07 2023 05:56:31
%S 72,108,128,200,256,288,392,432,500,512,576,648,675,800,864,968,972,
%T 1125,1152,1323,1352,1372,1568,1600,1728,1800,1944,2000,2048,2187,
%U 2304,2312,2592,2700,2888,2916,3087,3136,3200,3267,3456,3528,3872,3888,4000
%N Numbers of the form a^2*b^3, where a != b and a, b > 1.
%C Terms of A216427 that are not 5th powers of squarefree numbers (A113850) and not 10th powers of primes (A030629). - _Amiram Eldar_, Feb 07 2023
%H Charles R Greathouse IV, <a href="/A216426/b216426.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%t 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 *)
%t 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 *)
%o (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
%Y Cf. A143610.
%Y Subsequence of A216427. - _Zak Seidov_, Jan 03 2014
%Y Cf. A002117, A013661, A013663, A013664, A013668, A030629, A085966, A113850.
%K nonn
%O 1,1
%A _V. Raman_, Sep 07 2012
%E Name corrected by _Charles R Greathouse IV_, Jan 02 2014
|
