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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).
5
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
1,1
LINKS
EXAMPLE
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.
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);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Jul 04 2013
STATUS
approved