cp's OEIS Frontend

A230111 Composite numbers m such that Sum_{i=1..k} (p_i/(p_i+1)) - Product_{i=1..k} (p_i/(p_i-1)) is an integer, where p_i are the k prime factors of m (with multiplicity).

%I A230111 #8 Feb 14 2021 18:35:27
%S A230111 8,10,64,512,720,800,1320,1944,4096,5184,5760,6400,7200,8370,23520,
%T A230111 32768,41472,44000,46080,47040,51200,69580,74088,76096,84672,93000,
%U A230111 95040,105600,129360,235200,240000,262144,331776,368640,409600,518400,546480,576000,640000
%N A230111 Composite numbers m such that Sum_{i=1..k} (p_i/(p_i+1)) - Product_{i=1..k} (p_i/(p_i-1)) is an integer, where p_i are the k prime factors of m (with multiplicity).
%e A230111 Prime factors of 7200 are 2^5, 3^2 and 5^2.
%e A230111 Sum_{i=1..9} (p(i)/(p(i)+1)) = 5*(2/(2+1)) + 2*(3/(3+1)) + 2*(5/(5+1)) = 13/2.
%e A230111 Product_{i=1..9} (p(i)/(p(i)-1)) = (2/(2+1))^5 * (3/(3-1))^2 * (5/(5-1))^2 = 225/2.
%e A230111 Their sum is an integer: 13/2 - 225/2 = -106.
%p A230111 with(numtheory); P:=proc(i) local b,d,n,p;
%p A230111 for n from 2 to i do p:=ifactors(n)[2];
%p A230111 b:=add(op(2,d)*op(1,d)/(op(1,d)+1),d=p)-mul((op(1,d)/(op(1,d)-1))^op(2,d),d=p);
%p A230111 if trunc(b)=b then print(n); fi; od; end: P(10^7);
%Y A230111 Cf. A199767, A198391, A227034, A227248, A230110, A230112.
%K A230111 nonn
%O A230111 1,1
%A A230111 _Paolo P. Lava_, Oct 09 2013