A364750 - OEIS

%I #11 Aug 07 2023 02:11:37

%S 1,2,6,3326400,4989600,6652800,9979200,11793600,19958400,21621600,

%T 23284800,23587200,25945920,29937600,33264000,34927200,35380800,

%U 39916800,43243200,46569600,47174400,49896000,51891840,58968000,59875200,64864800,66528000,69854400,70761600,76204800,77837760,79833600

%N Integers k such that A000010(k) <= A008480(k).

%C Cameron asked whether there is an integer k with exactly 3 distinct prime factors such that A000010(k) < A008480(k). David Bevan found that the smallest example is 2^51 * 3^34 * 5^20 = 3.581...*10^45. - _Amiram Eldar_, Aug 06 2023

%H Peter Cameron's Blog, <a href="https://cameroncounts.wordpress.com/2023/02/17/an-exercise-in-number-theory/#comments">An exercise in number theory</a>, Posted on 17/02/2023.

%t g[p_, e_] := (p - 1)*p^(e - 1); q[n_] := Module[{f = FactorInteger[n]}, Times @@ g @@@ f <= Multinomial @@ f[[;; , 2]]]; Select[Range[10^7], q] (* _Amiram Eldar_, Aug 06 2023 *)

%o (PARI) m(n) = my(f=factor(n)[,2]); vecsum(f)!/prod(k=1, #f, f[k]!); \\ A008480

%o isok(n) = eulerphi(n) <= m(n);

%Y Cf. A000010, A008480.

%K nonn

%O 1,2

%A _Michel Marcus_, Aug 05 2023