A080670 Literal reading of the prime factorization of n.

1, 2, 3, 22, 5, 23, 7, 23, 32, 25, 11, 223, 13, 27, 35, 24, 17, 232, 19, 225, 37, 211, 23, 233, 52, 213, 33, 227, 29, 235, 31, 25, 311, 217, 57, 2232, 37, 219, 313, 235, 41, 237, 43, 2211, 325, 223, 47, 243, 72, 252, 317, 2213, 53, 233, 511, 237, 319, 229, 59, 2235

Offset

1,2

Comments

Exponents equal to 1 are omitted and therefore this sequence differs from A067599.

Here the first duplicate (ambiguous) term appears already with a(8)=23=a(6), in A067599 this happens only much later. - M. F. Hasler, Oct 18 2014

The number n = 13532385396179 = 13·53^2·3853·96179 = a(n) is (maybe the first?) nontrivial fixed point of this sequence, making it the first known index of a -1 in A195264. - M. F. Hasler, Jun 06 2017

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Tony Padilla and Brady Haran, 13532385396179, Numberphile Video, 2017

N. J. A. Sloane, Confessions of a Sequence Addict (AofA2017), slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.

N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

Example

8=2^3, which reads 23, hence a(8)=23; 12=2^2*3, which reads 223, hence a(12)=223.

Maple

ifsSorted := proc(n)
        local fs, L, p ;
        fs := sort(convert(numtheory[factorset](n), list)) ;
        L := [] ;
        for p in fs do
                L := [op(L), [p, padic[ordp](n, p)]] ;
        end do;
        L ;
end proc:
A080670 := proc(n)
        local a, p ;
        if n = 1 then
                return 1;
        end if;
        a := 0 ;
        for p in ifsSorted(n) do
                a := digcat2(a, op(1, p)) ;
                if op(2, p) > 1 then
                        a := digcat2(a, op(2, p)) ;
                end if;
        end do:
        a ;
end proc: # R. J. Mathar, Oct 02 2011
# second Maple program:
a:= proc(n) option remember; `if`(n=1, 1, (l->
      parse(cat(seq(`if`(l[i, 2]=1, l[i, 1], [l[i, 1],
      l[i, 2]][]), i=1..nops(l)))))(sort(ifactors(n)[2])))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 17 2020

Mathematica

f[n_] := FromDigits[ Flatten@ IntegerDigits[ Flatten[ FactorInteger@ n /. {1 -> {}}]]]; f[1] = 1; Array[ f, 60] (* Robert G. Wilson v, Mar 02 2003 and modified Jul 22 2014 *)

Prog

(PARI) A080670(n)=if(n>1, my(f=factor(n), s=""); for(i=1, #f~, s=Str(s, f[i, 1], if(f[i, 2]>1, f[i, 2], ""))); eval(s), 1) \\ Charles R Greathouse IV, Oct 27 2013; case n=1 added by M. F. Hasler, Oct 18 2014
(PARI) A080670(n)=if(n>1, eval(concat(apply(f->Str(f[1], if(f[2]>1, f[2], "")), Vec(factor(n)~)))), 1) \\ M. F. Hasler, Oct 18 2014
(Haskell)
import Data.Function (on)
a080670 1 = 1
a080670 n = read $ foldl1 (++) $
zipWith (c `on` show) (a027748_row n) (a124010_row n) :: Integer
where c ps es = if es == "1" then ps else ps ++ es
-- Reinhard Zumkeller, Oct 27 2013
(Python)
import sympy
[int(''.join([str(y) for x in sorted(sympy.ntheory.factorint(n).items()) for y in x if y != 1])) for n in range(2, 100)] # compute a(n) for n > 1
# Chai Wah Wu, Jul 15 2014

Crossrefs

Cf. A037276, A067599, A230305, A230625, A027748, A124010, A288818.

See A195330, A195331 for those n for which a(n) is a contraction.

See also home primes, A037271.

See A195264 for what happens when k -> a(k) is repeatedly applied to n.

Partial sums: A287881, A287882.

Sequence in context: A296254 A114749 A141458 * A288532 A073647 A073646

Adjacent sequences: A080667 A080668 A080669 * A080671 A080672 A080673

Keyword

nonn,base,look

Author

Jon Perry, Mar 02 2003

Extensions

Edited and extended by Robert G. Wilson v, Mar 02 2003

Status

approved