A140695 A number n is included if the number of positive divisors of n is neither a divisor of n nor is coprime to n.

6, 10, 14, 20, 22, 26, 28, 30, 32, 34, 38, 42, 44, 45, 46, 48, 50, 52, 54, 58, 62, 63, 66, 68, 70, 74, 75, 76, 78, 82, 86, 90, 92, 94, 98, 99, 102, 106, 110, 112, 114, 116, 117, 118, 120, 122, 124, 126, 130, 134, 138, 140, 142, 144, 146, 147, 148, 150, 153, 154, 158

Offset

1,1

Links

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

Example

36 has 9 divisors. 9 divides 36. So 36 is not in the sequence. 23 has 2 divisors. 2 is coprime to 23. So 23 is not in the sequence. On the other hand, 42 has 8 divisors. 8 does not divide 42. And 8 is not coprime to 42. So 42 is in the sequence.

Maple

filter:= proc(n) local t, g; t:= numtheory:-tau(n);
  g:= igcd(t, n);
  g > 1 and g < t
end proc:
select(filter, [$1..1000]); # Robert Israel, Apr 14 2017

Mathematica

Select[Range[200], 1 < Mod[ #, Length[Divisors[ # ]]] && GCD[ #, Length[Divisors[ # ]]] > 1 &] (* Stefan Steinerberger, May 30 2008 *)

Crossrefs

Cf. A140696.

Sequence in context: A315198 A006617 A246803 * A085681 A315199 A315200

Adjacent sequences: A140692 A140693 A140694 * A140696 A140697 A140698

Keyword

nonn

Author

Leroy Quet, May 23 2008

Extensions

More terms from Stefan Steinerberger, May 30 2008

Status

approved