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

1,2

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.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

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 *)

Prog

(PARI) isok(n)={my(f=factor(n)); vecprod(f[, 1]) >= sum(i=1, #f~, f[i, 1]*f[i, 2])} \\ Andrew Howroyd, Nov 20 2025

Crossrefs

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

Sequence in context: A375398 A317091 A048839 * A122144 A064052 A248792

Adjacent sequences: A360474 A360475 A360476 * A360478 A360479 A360480

Keyword

nonn

Author

Johan Lindgren, Feb 08 2023

Status

approved