A359869 Numbers whose product of distinct prime factors is less than the sum of its prime factors (with repetition).

4, 8, 9, 12, 16, 18, 24, 25, 27, 32, 36, 40, 48, 49, 50, 54, 64, 72, 80, 81, 96, 98, 100, 108, 112, 121, 125, 128, 144, 160, 162, 169, 192, 196, 200, 216, 224, 225, 242, 243, 250, 256, 288, 289, 320, 324, 338, 343, 361, 375, 384, 392, 400, 405, 432, 448, 484, 486, 500

Offset: 1

Author

Johan Lindgren, Jan 16 2023

Keywords

• nonn

Comments

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

Examples

			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.
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.
All prime numbers fail as terms since the product of distinct prime factors is equal to sum of prime factors.
		

Crossrefs

Cf. A001414, A007947.

Programs

Mathematica

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

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