A360477 Numbers whose product of distinct prime factors is greater than or equal to the sum of its prime factors (with repetition).

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

Offset: 1

Author

Johan Lindgren, Feb 08 2023

Keywords

• nonn

Comments

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

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

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

Examples

			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.
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.
		

Crossrefs

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

Programs

Mathematica

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 *)