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A359870
Numbers whose product of distinct prime factors is greater than the sum of its prime factors (with repetition).
2
1, 6, 10, 14, 15, 20, 21, 22, 26, 28, 30, 33, 34, 35, 38, 39, 42, 44, 45, 46, 51, 52, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 74, 75, 76, 77, 78, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 99, 102, 104, 105, 106, 110, 111, 114, 115, 116, 117
OFFSET
1,2
COMMENTS
Numbers k where A007947(k) > A001414(k).
No term is prime since in that case the product of distinct prime factors and the sum of prime factors are equal.
Composite squarefree numbers (A120944) form a subsequence, so squarefree semiprimes (A006881) also. - Bernard Schott, Feb 22 2023
LINKS
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.
MAPLE
filter:= proc(n) local F, t;
F:= ifactors(n)[2];
mul(t[1], t=F) > add(t[1]*t[2], t=F);
end proc:
select(f, [$1..1000]); # Robert Israel, Feb 07 2023
MATHEMATICA
q[n_] := Module[{f = FactorInteger[n]}, Times @@ f[[;; , 1]] > Plus @@ (f[[;; , 1]]*f[[;; , 2]])]; q[1] = True; Select[Range[120], 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
KEYWORD
nonn
AUTHOR
Johan Lindgren, Jan 16 2023
STATUS
approved