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

1,1

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

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

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

Cf. A006530, A020639, A088948, A088949.

Sequence in context: A228307 A179143 A176878 * A308643 A229094 A307108

Adjacent sequences: A088592 A088593 A088594 * A088596 A088597 A088598

Keyword

nonn

Author

Labos Elemer, Nov 20 2003

Status

approved