A036457 Numbers k for which exactly 5 applications of A000005 are needed to reach 2.

60, 72, 84, 90, 96, 108, 126, 132, 140, 150, 156, 160, 180, 198, 200, 204, 220, 224, 228, 234, 240, 252, 260, 276, 288, 294, 300, 306, 308, 315, 336, 340, 342, 348, 350, 352, 360, 364, 372, 380, 392, 396, 414, 416, 420, 432, 444, 450, 460, 468, 476, 480

Offset

1,1

Comments

Subsequences include A030630 (numbers with 12 divisors), A030636 (numbers with 18 divisors), A030638 (numbers with 20 divisors), A137491 (numbers with 28 divisors), etc. [edited by Jon E. Schoenfield, May 12 2018]

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

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

A036459(a(n)) = 5. - Ivan Neretin, Jan 25 2016

Example

a(13)=180; the successive iterates are 18, 6, 4, 3, and finally the 5th is 2;
a(3)=84; divisor numbers are 12, 6, 4, 3, and 2.

Maple

A036459:= proc(n) option remember;
  if n <= 2 then 0 else 1 + procname(numtheory:-tau(n)) fi
end proc:
select(A036459 = 5, [$1..1000]); # Robert Israel, Jan 25 2016

Mathematica

Select[Range@ 480, Last@ # == 2 && #[[5]] != 2 &@ NestList[DivisorSigma[0, #] &, #, 5] &] (* Michael De Vlieger, Jan 26 2016 *)

Prog

(PARI) is(n)=for(i=1, 4, n=numdiv(n); if(n<3, return(0))); numdiv(n)==2 \\ Charles R Greathouse IV, Sep 17 2015

Crossrefs

Cf. A000005, A007624, A036450, A036452, A036453, A036455, A030630.

Sequence in context: A216828 A345997 A131564 * A030630 A068350 A265712

Adjacent sequences: A036454 A036455 A036456 * A036458 A036459 A036460

Keyword

nonn

Author

Labos Elemer

Extensions

New name from Robert Israel, Jan 25 2016

Status

approved