OFFSET
1,1
EXAMPLE
Prime factors of 2200 are 2^3, 5^2 and 11.
Sum_{i=1..6} (p(i)/(p(i)+1)) = 3*(2/(2+1)) + 2*(5/(5+1)) + 11/(11+1) = 55/12.
Product_{i=1..6} (p(i)/(p(i)-1)) = (2/(2-1))^3*(5/(5-1))^2*11/(11-1) = 55/4.
The ratio is integer: (55/4) / (55/12) = 3.
MAPLE
with(numtheory); P:=proc(q) local a, d, n, p;
for n from 2 to q do if not isprime(n) then p:=ifactors(n)[2];
a:=mul((op(1, d)/(op(1, d)-1))^op(2, d), d=p)/add((op(1, d)/(op(1, d)+1))*op(2, d), d=p); if type(a, integer) then print(n); fi; fi;
od; end: P(10^7);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Oct 09 2013
STATUS
approved