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URL: https://oeis.org/A067599

⇱ A067599 - OEIS

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A067599
Decimal encoding of the prime factorization of n: concatenation of prime factors and exponents.
21
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
2,1
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
LINKS
EXAMPLE
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
MAPLE
with(ListTools): with(MmaTranslator[Mma]): seq(FromDigits(FlattenOnce(ifactors(n)[2])), n=2..46); # Wolfdieter Lang, Aug 16 2014
# Alternative:
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} ]
PROG
(PARI) A067599(n)=eval(concat(concat([""], concat(Vec(factor(n)~))~))) \\ M. F. Hasler, Oct 06 2013
(Haskell)
import Data.Function (on)
a067599 n = read $ foldl1 (++) $
zipWith ((++) `on` show) (a027748_row n) (a124010_row n) :: Integer
-- Reinhard Zumkeller, Oct 27 2013
(Python)
from sympy import factorint
def a(n): return int("".join(f"{p}{e}" for p, e in factorint(n).items()))
print([a(n) for n in range(2, 47)]) # Michael S. Branicky, Dec 11 2025
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Joseph L. Pe, Jan 31 2002
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
STATUS
approved