A227248 Composite numbers 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 n (with multiplicity).

4, 72, 102, 216, 260, 264, 270, 432, 462, 504, 612, 720, 1980, 2592, 3672, 5184, 5550, 8352, 10368, 15552, 20736, 22032, 25488, 29016, 30240, 31104, 36288, 38880, 41976, 46656, 49248, 57888, 62208, 93312, 103680, 132192, 186624, 238464, 286848, 373248, 410688

Offset: 1

Author

Paolo P. Lava, Jul 04 2013

Keywords

• nonn

Examples

			Prime factors of 270 are 2, 3^3, 5; therefore (2/(2+1)+3*3/(3+1)+5/(5+1))/(2/(2+1)*(3/(3+1))^3*5/(5+1)) = 16.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..65

Crossrefs

Cf. A224346, A224912, A226365, A227034.

Programs

Maple

with(numtheory); ListA227248:=proc(q) local a, d, n, p;
for n from 2 to q do if not isprime(n) then p:=ifactors(n)[2];
a:=add((op(1, d)/(op(1, d)+1))*op(2, d), d=p)/mul((op(1, d)/(op(1, d)+1))^op(2, d), d=p);
if type(a, integer) then print(n); fi; fi;
od; end: ListA227248(10^10);