

A084317


Concatenation of the prime factors of n, in increasing order.


18



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
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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*w1], {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



