A360477 - OEIS

%I #14 Feb 20 2023 07:52:11

%S 1,2,3,5,6,7,10,11,13,14,15,17,19,20,21,22,23,26,28,29,30,31,33,34,35,

%T 37,38,39,41,42,43,44,45,46,47,51,52,53,55,56,57,58,59,60,61,62,63,65,

%U 66,67,68,69,70,71,73,74,75,76,77,78,79,82,83,84,85,86,87,88,89,90,91,92,93,94,95

%N Numbers whose product of distinct prime factors is greater than or equal to the sum of its prime factors (with repetition).

%C Numbers k where A007947(k) >= A001414(k).

%C Similar to A359870 but also includes the primes (A000040).

%C All primes are terms since in that case the product of distinct prime factors and the sum of prime factors are equal.

%e 45 = 3^2*5 is a term since its product of distinct prime factors 3 * 5 = 15 is greater than its sum of prime factors with multiplicity 3 + 3 + 5 = 11.

%e 48 = 2^4*3 is not a term since its product of distinct prime factors 2 * 3 = 6 is less than its sum of prime factors with multiplicity 2 + 2 + 2 + 2 + 3 = 11.

%t q[n_] := Module[{f = FactorInteger[n]}, Times @@ f[[;; , 1]] >= Plus @@ (f[[;; , 1]]*f[[;; , 2]])]; q[1] = True; Select[Range[100], q] (* _Amiram Eldar_, Feb 08 2023 *)

%Y Cf. A000040, A001414, A007947, A359869, A359870.

%K nonn

%O 1,2

%A _Johan Lindgren_, Feb 08 2023