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A084317 Concatenation of the prime factors of n, in increasing order. 19
0, 2, 3, 2, 5, 23, 7, 2, 3, 25, 11, 23, 13, 27, 35, 2, 17, 23, 19, 25, 37, 211, 23, 23, 5, 213, 3, 27, 29, 235, 31, 2, 311, 217, 57, 23, 37, 219, 313, 25, 41, 237, 43, 211, 35, 223, 47, 23, 7, 25, 317, 213, 53, 23, 511, 27, 319, 229, 59, 235, 61, 231, 37, 2, 513, 2311, 67 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Prime factor set of n is concatenated as follows:

1. factorize n;

2. order prime factors without exponents in order of magnitude;

3. concatenate digits to get a(n) as a decimal number.

The choice a(1)=0 is conventional; a(1)=1 would have been another possible choice. - M. F. Hasler, Oct 21 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 0 since 1 has no prime factors to concatenate.

n = 2520 = 2*2*2*3*3*5*7; prime factor set = {2,3,5,7}, so a(2520) = 2357.

a(n) = a(squarefree kernel of n) = a(n^k) for any power k >= 1.

MAPLE

with(numtheory):

a:= n-> parse(cat(`if`(n=1, 0, sort([factorset(n)[]])[]))):

seq(a(n), n=1..100);  # Alois P. Heinz, Dec 06 2014

MATHEMATICA

ffi[x_] := Flatten[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] lf[x_] := Length[FactorInteger[x]] nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] conc[x_] := Fold[nd, 0, Flatten[IntegerDigits[ba[x]], 1]] Table[conc[w], {w, 1, 128}]

{0}~Join~Table[FromDigits@ Flatten@ IntegerDigits@ Map[First, FactorInteger@ n], {n, 2, 67}] (* Michael De Vlieger, May 02 2016 *)

PROG

(PARI) A084317(n)=if(n>1, eval(concat(apply(t->Str(t), factor(n)[, 1]~)))) \\ Unfortunately up to PARI version 2.7.1 at least, "Str" cannot be applied as a closure (= function), but Str = Str() = "". - M. F. Hasler, Oct 22 2014

CROSSREFS

Cf. A084318, A084319.

Sequence in context: A133568 A120716 A084318 * A037279 A163591 A085307

Adjacent sequences:  A084314 A084315 A084316 * A084318 A084319 A084320

KEYWORD

base,nonn,look

AUTHOR

Labos Elemer, Jun 16 2003

EXTENSIONS

Edited by M. F. Hasler, Oct 21 2014

STATUS

approved

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)