cp's OEIS Frontend

A359870 Numbers whose product of distinct prime factors is greater than the sum of its prime factors (with repetition).

%I A359870 #45 Feb 24 2023 04:54:22
%S A359870 1,6,10,14,15,20,21,22,26,28,30,33,34,35,38,39,42,44,45,46,51,52,55,
%T A359870 56,57,58,60,62,63,65,66,68,69,70,74,75,76,77,78,82,84,85,86,87,88,90,
%U A359870 91,92,93,94,95,99,102,104,105,106,110,111,114,115,116,117
%N A359870 Numbers whose product of distinct prime factors is greater than the sum of its prime factors (with repetition).
%C A359870 Numbers k where A007947(k) > A001414(k).
%C A359870 No term is prime since in that case the product of distinct prime factors and the sum of prime factors are equal.
%C A359870 Composite squarefree numbers (A120944) form a subsequence, so squarefree semiprimes (A006881) also. - _Bernard Schott_, Feb 22 2023
%H A359870 Robert Israel, <a href="/A359870/b359870.txt">Table of n, a(n) for n = 1..10000</a>
%e A359870 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.
%e A359870 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.
%p A359870 filter:= proc(n) local F,t;
%p A359870   F:= ifactors(n)[2];
%p A359870   mul(t[1],t=F) > add(t[1]*t[2],t=F);
%p A359870 end proc:
%p A359870 select(f, [$1..1000]); # _Robert Israel_, Feb 07 2023
%t A359870 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 *)
%o A359870 (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
%Y A359870 Cf. A001414, A007947, A359869.
%Y A359870 Cf. A006881, A120944.
%K A359870 nonn
%O A359870 1,2
%A A359870 _Johan Lindgren_, Jan 16 2023