A068936 Numbers having the sum of distinct prime factors not greater than the sum of exponents in prime factorization, A008472(n)<=A001222(n).

1, 4, 8, 16, 27, 32, 48, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 243, 256, 288, 320, 324, 384, 432, 486, 512, 576, 640, 648, 729, 768, 800, 864, 972, 1024, 1152, 1280, 1296, 1458, 1536, 1600, 1728, 1792, 1944, 2000, 2048, 2187, 2304, 2560, 2592, 2916

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Example

a(5) = 27 = 3^3, 3 = 3;
a(10) = 81 = 3^4, 3 < 4;
a(100) = 16000 = 2^7 * 5^3,  2+5 < 7+3;
a(1000) = 10321920 = 2^15 * 3^2 * 5 * 7, 2+3+5+7 < 15+2+1+1.

Mathematica

fQ[n_] := Block[{f = FactorInteger@n}, Plus @@ Last /@ f >= Plus @@ First /@ f]; Select[ Range@3000, fQ@ # &] (* Robert G. Wilson v *)
Select[Range@ 3000, First@ Differences@ Map[Total, Transpose@ FactorInteger@ #] >= 0 &] (* Michael De Vlieger, Dec 08 2016 *)

Prog

(Haskell)
a068936 n = a068936_list !! (n-1)
a068936_list = [x | x <- [1..], a008472 x <= a001222 x]
-- Reinhard Zumkeller, Nov 10 2013

Crossrefs

Cf. A068935, A054411, A068937, A068938.

Sequence in context: A331243 A180861 A353316 * A345329 A349112 A325127

Adjacent sequences: A068933 A068934 A068935 * A068937 A068938 A068939

Keyword

nonn

Author

Reinhard Zumkeller, Mar 08 2002

Extensions

More terms from Robert G. Wilson v, Jan 16 2006

Status

approved