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A037278 Replace n with concatenation of its divisors.

%I A037278 #59 Feb 21 2025 05:49:38
%S A037278 1,12,13,124,15,1236,17,1248,139,12510,111,1234612,113,12714,13515,
%T A037278 124816,117,1236918,119,12451020,13721,121122,123,1234681224,1525,
%U A037278 121326,13927,12471428,129,12356101530,131,12481632,131133,121734,15735,123469121836,137
%N A037278 Replace n with concatenation of its divisors.
%C A037278 a(n) is the union of A176555(n) for n >= 1 and A176556(n) for n >= 2. See A176553 (numbers m such that concatenations of divisors of m are noncomposites) and A176554 (numbers m such that concatenations of divisors of m are nonprimes). [_Jaroslav Krizek_, Apr 21 2010]
%C A037278 a(n) is the concatenation of n-th row of the triangle in A027750.
%H A037278 Reinhard Zumkeller, <a href="/A037278/b037278.txt">Table of n, a(n) for n = 1..10000</a>
%F A037278 A134681(n) = A055642(a(n)). - _Reinhard Zumkeller_, Nov 06 2007
%t A037278 a[n_] := ToExpression[ StringJoin[ ToString /@ Divisors[n] ] ]; Table[ a[n], {n, 1, 34}] (* _Jean-François Alcover_, Dec 01 2011 *)
%t A037278 FromDigits[Flatten[IntegerDigits/@Divisors[#]]]&/@Range[40] (* _Harvey P. Dale_, Nov 09 2012 *)
%o A037278 (Haskell)
%o A037278 a037278 = read . concatMap show . a027750_row :: Integer -> Integer
%o A037278 -- _Reinhard Zumkeller_, Jul 13 2013, May 01 2012, Aug 07 2011
%o A037278 (PARI) a(n) = my(s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ _Michel Marcus_, Jun 01 2019 and Sep 22 2022
%o A037278 (Magma) k:=1; sol:=[];
%o A037278 for u in [1..34] do D:=Divisors(u); conc:=D[1];
%o A037278     for u1 in [2..#D] do a:=#Intseq(conc); a1:=#Intseq(D[u1]); conc:=10^a1*conc+D[u1];end for;
%o A037278      sol[u]:=conc; k:=k+1;
%o A037278 end for;
%o A037278 sol; // _Marius A. Burtea_, Jun 01 2019
%o A037278 (MATLAB) m=1;
%o A037278 for u=1:34 div=divisors(u); conc=str2num(strrep(num2str(div), ' ', ''));
%o A037278    sol(m)=conc; m=m+1;
%o A037278 end
%o A037278 sol % _Marius A. Burtea_, Jun 01 2019
%o A037278 (Python)
%o A037278 from sympy import divisors
%o A037278 def a(n): return int("".join(str(d) for d in divisors(n)))
%o A037278 print([a(n) for n in range(1, 35)]) # _Michael S. Branicky_, Dec 31 2020
%Y A037278 Cf. A027750, A037283, A037277, A106708.
%K A037278 nonn,easy,base,nice
%O A037278 1,2
%A A037278 _N. J. A. Sloane_
%E A037278 More terms from _Erich Friedman_