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

1,2

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Illustration of the first terms

Example

See illustration of the first terms in Links section.

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 *)

Prog

(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)))

Crossrefs

Cf. A080670, A182318.

Sequence in context: A114749 A141458 A080670 * A073647 A073646 A037276

Adjacent sequences: A288529 A288530 A288531 * A288533 A288534 A288535

Keyword

nonn,base

Author

Rémy Sigrist, Jun 11 2017

Status

approved