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

6, 8, 10, 14, 15, 21, 22, 26, 27, 33, 34, 35, 36, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 120, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 168, 177, 178, 183

Offset

1,1

Comments

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.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

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

A036459(a(n)) = 3. - Ivan Neretin, Jan 25 2016

Example

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.

Maple

filter:= proc(n) local r;
  r:= numtheory:-tau(numtheory:-tau(n));
  r::odd and isprime(r)
end proc:
select(filter, [$1..1000]); # Robert Israel, Feb 02 2016

Mathematica

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

Prog

(PARI) is(n)=isprime(n=numdiv(numdiv(n))) && n>2 \\ Charles R Greathouse IV, Jan 22 2013

Crossrefs

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

Sequence in context: A365535 A120497 A036436 * A291127 A211337 A007422

Adjacent sequences: A036452 A036453 A036454 * A036456 A036457 A036458

Keyword

nonn

Author

Labos Elemer

Extensions

Definition clarified by R. J. Mathar and Charles R Greathouse IV, Jan 22 2013

Status

approved