A068936 - OEIS

%I #17 Dec 08 2016 11:31:25

%S 1,4,8,16,27,32,48,64,72,81,96,108,128,144,162,192,216,243,256,288,

%T 320,324,384,432,486,512,576,640,648,729,768,800,864,972,1024,1152,

%U 1280,1296,1458,1536,1600,1728,1792,1944,2000,2048,2187,2304,2560,2592,2916

%N Numbers having the sum of distinct prime factors not greater than the sum of exponents in prime factorization, A008472(n)<=A001222(n).

%H Reinhard Zumkeller, <a href="/A068936/b068936.txt">Table of n, a(n) for n = 1..1000</a>

%e a(5) = 27 = 3^3, 3 = 3;

%e a(10) = 81 = 3^4, 3 < 4;

%e a(100) = 16000 = 2^7 * 5^3,  2+5 < 7+3;

%e a(1000) = 10321920 = 2^15 * 3^2 * 5 * 7, 2+3+5+7 < 15+2+1+1.

%t fQ[n_] := Block[{f = FactorInteger@n}, Plus @@ Last /@ f >= Plus @@ First /@ f]; Select[ Range@3000, fQ@ # &] (* _Robert G. Wilson v_ *)

%t Select[Range@ 3000, First@ Differences@ Map[Total, Transpose@ FactorInteger@ #] >= 0 &] (* _Michael De Vlieger_, Dec 08 2016 *)

%o (Haskell)

%o a068936 n = a068936_list !! (n-1)

%o a068936_list = [x | x <- [1..], a008472 x <= a001222 x]

%o -- _Reinhard Zumkeller_, Nov 10 2013

%Y Cf. A068935, A054411, A068937, A068938.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Mar 08 2002

%E More terms from _Robert G. Wilson v_, Jan 16 2006