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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A130763 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

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Last modified April 26 09:52 EDT 2019. Contains 322472 sequences. (Running on oeis4.)