A359869 - OEIS

%I #19 Jan 20 2023 09:03:24

%S 4,8,9,12,16,18,24,25,27,32,36,40,48,49,50,54,64,72,80,81,96,98,100,

%T 108,112,121,125,128,144,160,162,169,192,196,200,216,224,225,242,243,

%U 250,256,288,289,320,324,338,343,361,375,384,392,400,405,432,448,484,486,500

%N Numbers whose product of distinct prime factors is less than the sum of its prime factors (with repetition).

%C Numbers n where A007947(n) < A001414(n).

%e 12 = 2^2*3 is a term since its product of distinct prime factors 2 * 3 = 6 is less than its sum of prime factors with multiplicity 2 + 2 + 3 = 7.

%e 45 = 3^2*5 is not 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 All prime numbers fail as terms since the product of distinct prime factors is equal to sum of prime factors.

%t q[n_] := Module[{f = FactorInteger[n]}, Times @@ f[[;; , 1]] < Plus @@ (f[[;; , 1]]*f[[;; , 2]])]; Select[Range[500], q] (* _Amiram Eldar_, Jan 16 2023 *)

%o (PARI) isok(n)={my(f=factor(n)); vecprod(f[, 1]) < sum(i=1, #f~, f[i, 1]*f[i, 2])} \\ _Andrew Howroyd_, Jan 16 2023

%Y Cf. A001414, A007947.

%K nonn

%O 1,1

%A _Johan Lindgren_, Jan 16 2023