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A036456 Numbers k for which exactly 4 applications of A000005 are needed to reach 2. 2

%I

%S 12,18,20,24,28,30,32,40,42,44,45,48,50,52,54,56,63,66,68,70,75,76,78,

%T 80,88,92,98,99,102,104,105,110,112,114,116,117,124,128,130,135,136,

%U 138,144,147,148,152,153,154,162,164,165,170,171,172,174,175,176,182

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

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

%H Amiram Eldar, <a href="/A036456/b036456.txt">Table of n, a(n) for n = 1..10000</a>

%F With d(n) = number of divisors(n), d(d(d(d(a(n))))) = 2 and d(d(d(a(n)))) > 2.

%F A036459(a(n)) = 4. - _Ivan Neretin_, Jan 25 2016

%e 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.

%o (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

%Y Cf. A000005, A007624, A036450, A036453, A036455, A046452.

%K nonn

%O 1,1

%A _Labos Elemer_

%E New name (using new name for A036457 from _Robert Israel_) from _Jon E. Schoenfield_, May 12 2018

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Last modified June 4 01:54 EDT 2020. Contains 334812 sequences. (Running on oeis4.)