A227034 Composite numbers such that product_{i=1..k} (p_i/(p_i-1)) / sum_{i=1..k} (p_i/(p_i-1)) is an integer, where p_i are the k prime factors of n (with multiplicity).

4, 16, 72, 132, 256, 800, 1232, 2208, 2960, 5184, 5376, 11904, 19200, 23760, 39040, 41472, 65536, 72000, 76032, 76800, 84816, 203280, 259200, 288768, 332928, 345600, 373248, 383040, 416000, 614400, 628992, 640000, 663552, 691200, 1228800, 1996800, 2013312

Offset: 1

Author

Paolo P. Lava, Jul 03 2013

Keywords

• nonn

Comments

All terms are even numbers.

Examples

			Prime factors of 1232 are 2^4, 7, 11 and ((2/(2-1))^4*7/(7-1)*11/(11-1)) / (4*2/(2-1)+7/(7-1)+11/(11-1)) = 2.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A224346, A224912, A226365, A227248.

Programs

Maple

with(numtheory); ListA226365:=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: ListA226365(10^10);