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.

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

Author

Labos Elemer, Nov 20 2003

Keywords

• nonn

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

Examples

			n = 315 = 3*3*5*7 is not a power of a prime, has 3 prime factors and (3+5)/2=7 divides n.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A020639, A088948, A088949.

Programs

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 *)