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A037276 Start with 1; for n>1, replace n with the concatenation of its prime factors in increasing order. 19

%I

%S 1,2,3,22,5,23,7,222,33,25,11,223,13,27,35,2222,17,233,19,225,37,211,

%T 23,2223,55,213,333,227,29,235,31,22222,311,217,57,2233,37,219,313,

%U 2225,41,237,43,2211,335,223,47,22223,77,255,317,2213,53,2333

%N Start with 1; for n>1, replace n with the concatenation of its prime factors in increasing order.

%H N. J. A. Sloane, <a href="/A037276/b037276.txt">Table of n, a(n) for n = 1..20000</a> [First 10000 terms from T. D. Noe]

%H P. De Geest, <a href="http://www.worldofnumbers.com/topic1.htm">Home Primes</a>

%H N. J. A. Sloane, <a href="/A195264/a195264.pdf">Confessions of a Sequence Addict (AofA2017)</a>, slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.

%H N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, <a href="https://vimeo.com/237029685">Part I</a>, <a href="https://vimeo.com/237030304">Part 2</a>, <a href="https://oeis.org/A290447/a290447_slides.pdf">Slides.</a> (Mentions this sequence)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HomePrime.html">Home Prime</a>

%e If n = 2^3*5^5*11^2 = 3025000, a(n) = 222555551111 (n=2*2*2*5*5*5*5*5*11*11, then remove the multiplication signs).

%p # This is for n>1

%p read("transforms") ;

%p A037276 := proc(n)

%p local L,p ;

%p L := [] ;

%p for p in ifactors(n)[2] do

%p L := [op(L),seq(op(1,p),i=1..op(2,p))] ;

%p end do:

%p digcatL(L) ;

%p end proc: # _R. J. Mathar_, Oct 29 2012

%t co[n_, k_] := Nest[Flatten[IntegerDigits[{#, n}]] &, n, k - 1]; Table[FromDigits[Flatten[IntegerDigits[co @@@ FactorInteger[n]]]], {n, 54}] (* _Jayanta Basu_, Jul 04 2013 *)

%t FromDigits@ Flatten@ IntegerDigits[Table[#1, {#2}] & @@@ FactorInteger@ #] & /@ Range@ 54 (* _Michael De Vlieger_, Jul 14 2015 *)

%o (PARI) a(n)={ n<4 & return(n); for(i=1,#n=factor(n)~, n[1,i]=concat(vector(n[2,i],j,Str(n[1,i])))); eval(concat(n[1,]))} \\ _M. F. Hasler_, Jun 19 2011

%o (Haskell)

%o a037276 = read . concatMap show . a027746_row

%o -- _Reinhard Zumkeller_, Apr 03 2012

%o (Python)

%o from sympy import factorint

%o def a(n):

%o f=factorint(n)

%o l=sorted([i for i in f])

%o return 1 if n==1 else int("".join([str(i)*f[i] for i in l]))

%o print [a(n) for n in xrange(1, 101)] # _Indranil Ghosh_, Jun 23 2017

%Y Cf. A037274, A048985, A067599, A080670, A084796. Different from A073646.

%Y Cf. also A027746, A289660 (a(n)-n).

%K nonn,easy,base

%O 1,2

%A _N. J. A. Sloane_

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Last modified January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)