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

Author

Labos Elemer

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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

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

Extensions

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