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Numbers n such that d(d(n)) is an odd prime, where d(k) is the number of divisors of k.
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%I #22 Feb 04 2016 15:58:42

%S 6,8,10,14,15,21,22,26,27,33,34,35,36,38,39,46,51,55,57,58,62,65,69,

%T 74,77,82,85,86,87,91,93,94,95,100,106,111,115,118,119,120,122,123,

%U 125,129,133,134,141,142,143,145,146,155,158,159,161,166,168,177,178,183

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

%C 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 Charles R Greathouse IV, <a href="/A036455/b036455.txt">Table of n, a(n) for n = 1..10000</a>

%F d(d(d(a(n)))) = 2 for all n.

%F A036459(a(n)) = 3. - _Ivan Neretin_, Jan 25 2016

%e 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 filter:= proc(n) local r;

%p r:= numtheory:-tau(numtheory:-tau(n));

%p r::odd and isprime(r)

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Feb 02 2016

%t fQ[n_] := Module[{d2 = DivisorSigma[0, DivisorSigma[0, n]]}, d2 > 2 && PrimeQ[d2]]; Select[Range[200], fQ] (* _T. D. Noe_, Jan 22 2013 *)

%o (PARI) is(n)=isprime(n=numdiv(numdiv(n))) && n>2 \\ _Charles R Greathouse IV_, Jan 22 2013

%Y Cf. A000005, A007422, A030513, A036450, A036452, A036454, A036456, A036457, A036458.

%K nonn

%O 1,1

%A _Labos Elemer_

%E Definition clarified by _R. J. Mathar_ and _Charles R Greathouse IV_, Jan 22 2013