A067599 Decimal encoding of the prime factorization of n: concatenation of prime factors and exponents.

21, 31, 22, 51, 2131, 71, 23, 32, 2151, 111, 2231, 131, 2171, 3151, 24, 171, 2132, 191, 2251, 3171, 21111, 231, 2331, 52, 21131, 33, 2271, 291, 213151, 311, 25, 31111, 21171, 5171, 2232, 371, 21191, 31131, 2351, 411, 213171, 431, 22111, 3251, 21231

Offset: 2

Author

Joseph L. Pe, Jan 31 2002

Keywords

• base
• easy
• nonn

Comments

If n has prime factorization p_1^e_1 * ... * p_r^e_r with p_1 < ... < p_r, then its decimal encoding is p_1 e_1...p_r e_r. For example, 15 = 3^1 * 5^1, so has decimal encoding 3151.

Sequence A068633 is a duplicate, up to a conventional initial term a(1)=11.

a(31) = a(177147) = 311. Is there any solution to a(n) = n? - Franklin T. Adams-Watters, Dec 18 2006

The earliest duplicate is a(223) = 2231 = a(12). There is no fixed point below 3*10^6. - M. F. Hasler, Oct 06 2013

Examples

			The prime factorization of 24 = 2^3 * 3^1 has corresponding encoding 2331. So a(24) = 2331.
a(42) = 213171 since 42 = 2^1*3^1*7^1. - _Amarnath Murthy_, Feb 27 2002
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A037276, A080670, A112375.

Cf. A027748, A124010.

Programs

Haskell

import Data.Function (on)
a067599 n = read $ foldl1 (++) $
   zipWith ((++) `on` show) (a027748_row n) (a124010_row n) :: Integer
-- Reinhard Zumkeller, Oct 27 2013

Maple

with(ListTools): with(MmaTranslator[Mma]): seq(FromDigits(FlattenOnce(ifactors(n)[2])), n=2..46); # Wolfdieter Lang, Aug 16 2014
# second Maple program:
a:= n-> parse(cat(map(i-> i[], sort(ifactors(n)[2]))[])):
seq(a(n), n=2..60);  # Alois P. Heinz, Mar 16 2018

Mathematica

f[n_] := FromDigits[ Flatten[ IntegerDigits[ FactorInteger[ n]]]]; Table[ f[n], {n, 2, 50} ]

PARI

A067599(n)=eval(concat(concat([""],concat(Vec(factor(n)~))~))) \\ - M. F. Hasler, Oct 06 2013

Extensions

Edited by Robert G. Wilson v, Feb 02 2002

Merged contributions from A068633 to here, and minor edits by M. F. Hasler, Oct 06 2013