OFFSET
1,1
EXAMPLE
Prime factors of 7200 are 2^5, 3^2 and 5^2.
Sum_{i=1..9} (p(i)/(p(i)+1)) = 5*(2/(2+1)) + 2*(3/(3+1)) + 2*(5/(5+1)) = 13/2.
Product_{i=1..9} (p(i)/(p(i)-1)) = (2/(2+1))^5 * (3/(3-1))^2 * (5/(5-1))^2 = 225/2.
Their sum is an integer: 13/2 - 225/2 = -106.
MAPLE
with(numtheory); P:=proc(i) local b, d, n, p;
for n from 2 to i do p:=ifactors(n)[2];
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);
if trunc(b)=b then print(n); fi; od; end: P(10^7);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Oct 09 2013
STATUS
approved