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%I #9 Jun 13 2017 09:18:53
%S 1,2,3,22,5,23,7,23,32,25,11,223,13,27,35,222,17,232,19,225,37,211,23,
%T 233,52,213,33,227,29,235,31,25,311,217,57,2232,37,219,313,235,41,237,
%U 43,2211,325,223,47,2223,72,252,317,2213,53,233,511,237,319,229
%N Literal reading of the prime tower factorization of n.
%C The prime tower factorization of a number is defined in A182318.
%C The sequence is similar to A080670; however here we recursively factorize prime exponents.
%C a(1) = 1 by convention.
%C a(p) = p for any prime p.
%C As for A080670, 13532385396179 is a composite fixed point.
%H Rémy Sigrist, <a href="/A288532/b288532.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A288532/a288532.pdf">Illustration of the first terms</a>
%e See illustration of the first terms in Links section.
%t Array[FromDigits@ Flatten@ Map[IntegerDigits, DeleteCases[#, 1] /. {} -> {1}] &@ Flatten@ FixedPoint[Map[If[PrimeQ@ Last@ # || Last@ # == 1, #, {First@ #, FactorInteger@ Last@ #}] &, #, {Depth@ # - 2}] &, FactorInteger@ #] &, 58] (* or *)
%t Table[FromDigits@ Flatten@ Map[IntegerDigits, DeleteCases[ Flatten[ FactorInteger[n] //. {p_, e_} /; e > 1 :> {p, FactorInteger@ e}], 1] /. {} -> {1}], {n, 58}] (* _Michael De Vlieger_, Jun 11 2017 *)
%o (PARI) a(n) = my (s="", f=factor(n)); for (i=1, #f~, s=concat(s,Str(f[i,1])); if (f[i,2]>1, s=concat(s,Str(a(f[i,2]))))); return (if(s=="", 1, eval(s)))
%Y Cf. A080670, A182318.
%K nonn,base
%O 1,2
%A _Rémy Sigrist_, Jun 11 2017
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