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

1,1

Comments

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

Links

Table of n, a(n) for n=1..59.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A001414, A007947.

Sequence in context: A322109 A122145 A328014 * A034030 A057109 A369639

Adjacent sequences: A359866 A359867 A359868 * A359870 A359871 A359872

Keyword

nonn

Author

Johan Lindgren, Jan 16 2023

Status

approved