A084317 Concatenation of the prime factors of n, in increasing order.

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

Offset: 1

Author

Labos Elemer, Jun 16 2003

Keywords

• base
• nonn
• look

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A084318, A084319.

Programs

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 *)

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

Formula

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

Extensions

Edited by M. F. Hasler, Oct 21 2014