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A360477
Numbers whose product of distinct prime factors is greater than or equal to the sum of its prime factors (with repetition).
0
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
1,2
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.
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Johan Lindgren, Feb 08 2023
STATUS
approved