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A036455 Numbers n such that d(d(n)) is an odd prime, where d(k) is the number of divisors of k.

%I A036455 #22 Feb 04 2016 15:58:42
%S A036455 6,8,10,14,15,21,22,26,27,33,34,35,36,38,39,46,51,55,57,58,62,65,69,
%T A036455 74,77,82,85,86,87,91,93,94,95,100,106,111,115,118,119,120,122,123,
%U A036455 125,129,133,134,141,142,143,145,146,155,158,159,161,166,168,177,178,183
%N A036455 Numbers n such that d(d(n)) is an odd prime, where d(k) is the number of divisors of k.
%C A036455 Compare with sequence A007422 and A030513 -- the resemblance is rather strong. Still this sequence is different. For example, 36, 100, 120, and 168 are here.
%H A036455 Charles R Greathouse IV, <a href="/A036455/b036455.txt">Table of n, a(n) for n = 1..10000</a>
%F A036455 d(d(d(a(n)))) = 2 for all n.
%F A036455 A036459(a(n)) = 3. - _Ivan Neretin_, Jan 25 2016
%e A036455 a(15) = 39 and d(39) = 4, d(d(39)) = d(4) = 3 and d(d(d(39))) = 2. After 3 iteration the equilibrium is reached.
%p A036455 filter:= proc(n) local r;
%p A036455   r:= numtheory:-tau(numtheory:-tau(n));
%p A036455   r::odd and isprime(r)
%p A036455 end proc:
%p A036455 select(filter, [$1..1000]); # _Robert Israel_, Feb 02 2016
%t A036455 fQ[n_] := Module[{d2 = DivisorSigma[0, DivisorSigma[0, n]]}, d2 > 2 && PrimeQ[d2]]; Select[Range[200], fQ] (* _T. D. Noe_, Jan 22 2013 *)
%o A036455 (PARI) is(n)=isprime(n=numdiv(numdiv(n))) && n>2 \\ _Charles R Greathouse IV_, Jan 22 2013
%Y A036455 Cf. A000005, A007422, A030513, A036450, A036452, A036454, A036456, A036457, A036458.
%K A036455 nonn
%O A036455 1,1
%A A036455 _Labos Elemer_
%E A036455 Definition clarified by _R. J. Mathar_ and _Charles R Greathouse IV_, Jan 22 2013