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A080670 Literal reading of the prime factorization of n. 12
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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

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

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

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.

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

See also home primes, A037271.

Cf. A027748, A124010.

Sequence in context: A090122 A114749 A141458 * A073647 A073646 A037276

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

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Last modified May 29 13:14 EDT 2017. Contains 287247 sequences.