

A036456


Numbers k for which exactly 4 applications of A000005 are needed to reach 2.


2



12, 18, 20, 24, 28, 30, 32, 40, 42, 44, 45, 48, 50, 52, 54, 56, 63, 66, 68, 70, 75, 76, 78, 80, 88, 92, 98, 99, 102, 104, 105, 110, 112, 114, 116, 117, 124, 128, 130, 135, 136, 138, 144, 147, 148, 152, 153, 154, 162, 164, 165, 170, 171, 172, 174, 175, 176, 182
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OFFSET

1,1


COMMENTS

Similar to but different from A007624. Terms like 60, 72, 84, 90, 96, 108, 126, etc. are not present here.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


FORMULA

With d(n) = number of divisors(n), d(d(d(d(a(n))))) = 2 and d(d(d(a(n)))) > 2.
A036459(a(n)) = 4.  Ivan Neretin, Jan 25 2016


EXAMPLE

a(3)=20 and a(17)=63; for both x=20 and 63, d(x)=6 and d(d(x))=4, the 3rd iterates are 3 and the equilibrium value, i.e., 2 appears as 4th iterates.


PROG

(PARI) isok(n) = ((nd=numdiv(n)) != 2) && ((nd=numdiv(nd)) != 2) && ((nd=numdiv(nd)) != 2) && ((nd=numdiv(nd)) == 2); \\ Michel Marcus, Dec 30 2013 & Jan 26 2015


CROSSREFS

Cf. A000005, A007624, A036450, A036453, A036455, A046452.
Sequence in context: A319229 A271345 A007624 * A102467 A126706 A123711
Adjacent sequences: A036453 A036454 A036455 * A036457 A036458 A036459


KEYWORD

nonn


AUTHOR

Labos Elemer


EXTENSIONS

New name (using new name for A036457 from Robert Israel) from Jon E. Schoenfield, May 12 2018


STATUS

approved



