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

%I A037276 #60 Feb 16 2025 08:32:37
%S A037276 1,2,3,22,5,23,7,222,33,25,11,223,13,27,35,2222,17,233,19,225,37,211,
%T A037276 23,2223,55,213,333,227,29,235,31,22222,311,217,57,2233,37,219,313,
%U A037276 2225,41,237,43,2211,335,223,47,22223,77,255,317,2213,53,2333
%N A037276 Start with 1; for n>1, replace n with the concatenation of its prime factors in increasing order.
%H A037276 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 A037276 Patrick De Geest, <a href="http://www.worldofnumbers.com/topic1.htm">Home Primes</a>
%H A037276 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 A037276 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 A037276 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HomePrime.html">Home Prime</a>
%e A037276 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 A037276 # This is for n>1
%p A037276 read("transforms") ;
%p A037276 A037276 := proc(n)
%p A037276     local L,p ;
%p A037276     L := [] ;
%p A037276     for p in ifactors(n)[2] do
%p A037276         L := [op(L),seq(op(1,p),i=1..op(2,p))] ;
%p A037276     end do:
%p A037276     digcatL(L) ;
%p A037276 end proc: # _R. J. Mathar_, Oct 29 2012
%t A037276 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 A037276 FromDigits@ Flatten@ IntegerDigits[Table[#1, {#2}] & @@@ FactorInteger@ #] & /@ Range@ 54 (* _Michael De Vlieger_, Jul 14 2015 *)
%o A037276 (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 A037276 (Haskell)
%o A037276 a037276 = read . concatMap show . a027746_row
%o A037276 -- _Reinhard Zumkeller_, Apr 03 2012
%o A037276 (Python)
%o A037276 from sympy import factorint
%o A037276 def a(n):
%o A037276     f=factorint(n)
%o A037276     l=sorted(f)
%o A037276     return 1 if n==1 else int("".join(str(i)*f[i] for i in l))
%o A037276 print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jun 23 2017
%Y A037276 Cf. A037274, A048985, A067599, A080670, A084796. Different from A073646.
%Y A037276 Cf. also A027746, A289660 (a(n)-n).
%K A037276 nonn,easy,base
%O A037276 1,2
%A A037276 _N. J. A. Sloane_