A036456 Numbers k for which exactly 4 applications of A000005 are needed to reach 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

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, A036452, A036453, A036455.

Sequence in context: A334160 A271345 A007624 * A102467 A342973 A126706

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