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A080670 Literal reading of the prime factorization of n. 26
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
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
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
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
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 March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)