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A288532 Literal reading of the prime tower factorization of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)