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

1,2

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

Formula

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

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.

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: A375288 A120716 A084318 * A361320 A037279 A163591

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