A288532 Literal reading of the prime tower factorization of n.

1, 2, 3, 22, 5, 23, 7, 23, 32, 25, 11, 223, 13, 27, 35, 222, 17, 232, 19, 225, 37, 211, 23, 233, 52, 213, 33, 227, 29, 235, 31, 25, 311, 217, 57, 2232, 37, 219, 313, 235, 41, 237, 43, 2211, 325, 223, 47, 2223, 72, 252, 317, 2213, 53, 233, 511, 237, 319, 229

Offset: 1

Author

Rémy Sigrist, Jun 11 2017

Keywords

• nonn
• base

Comments

The prime tower factorization of a number is defined in A182318.

The sequence is similar to A080670; however here we recursively factorize prime exponents.

a(1) = 1 by convention.

a(p) = p for any prime p.

As for A080670, 13532385396179 is a composite fixed point.

Examples

			See illustration of the first terms in Links section.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Illustration of the first terms

Crossrefs

Cf. A080670, A182318.

Programs

Mathematica

Array[FromDigits@ Flatten@ Map[IntegerDigits, DeleteCases[#, 1] /. {} -> {1}] &@ Flatten@ FixedPoint[Map[If[PrimeQ@ Last@ # || Last@ # == 1, #, {First@ #, FactorInteger@ Last@ #}] &, #, {Depth@ # - 2}] &, FactorInteger@ #] &, 58] (* or *)
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 *)

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)))