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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
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
New name (using new name for A036457 from Robert Israel) from Jon E. Schoenfield, May 12 2018
STATUS
approved