A140695 - OEIS

%I #11 Apr 14 2017 03:09:49

%S 6,10,14,20,22,26,28,30,32,34,38,42,44,45,46,48,50,52,54,58,62,63,66,

%T 68,70,74,75,76,78,82,86,90,92,94,98,99,102,106,110,112,114,116,117,

%U 118,120,122,124,126,130,134,138,140,142,144,146,147,148,150,153,154,158

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

%H Robert Israel, <a href="/A140695/b140695.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p filter:= proc(n) local t,g; t:= numtheory:-tau(n);

%p   g:= igcd(t,n);

%p   g > 1 and g < t

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Apr 14 2017

%t Select[Range[200], 1 < Mod[ #, Length[Divisors[ # ]]] && GCD[ #, Length[Divisors[ # ]]] > 1 &] (* _Stefan Steinerberger_, May 30 2008 *)

%Y Cf. A140696.

%K nonn

%O 1,1

%A _Leroy Quet_, May 23 2008

%E More terms from _Stefan Steinerberger_, May 30 2008