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A088595
Numbers n such that (A006530(n) + A020639(n))/2 is an integer, divides n and it is not a power of prime number: it has at least 2 distinct prime factors. Special terms of A088948.
4
105, 231, 315, 525, 627, 693, 735, 897, 935, 945, 1155, 1575, 1581, 1617, 1729, 1881, 2079, 2205, 2465, 2541, 2625, 2691, 2835, 2967, 3135, 3465, 3525, 3675, 4123, 4301, 4389, 4485, 4675, 4715, 4725, 4743, 4851, 5145, 5487, 5643, 5775, 6237, 6279, 6545
OFFSET
1,1
COMMENTS
Every number of the sequence has at least three different prime factors. Also, the sequence is infinite (it contains all numbers of the form 3^a*5^b*7^c with a,b,c>0). - Emmanuel Vantieghem, Nov 21 2016
LINKS
EXAMPLE
n = 315 = 3*3*5*7 is not a power of a prime, has 3 prime factors and (3+5)/2=7 divides n.
MAPLE
filter:= proc(n) local F;
F:= numtheory:-factorset(n);
nops(F) > 2 and n mod (min(F)+max(F))/2 = 0
end proc:
select(filter, [seq(i, i=1..10^4, 2)]); # Robert Israel, Nov 21 2016
MATHEMATICA
Rest@ Select[Range@ 6600, Function[n, And[IntegerQ@ #, Divisible[n, #], ! PrimePowerQ@ n] &[(#[[-1, 1]] + #[[1, 1]])/2] &@ FactorInteger@ n]] (* Michael De Vlieger, Nov 24 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 20 2003
STATUS
approved