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A037278 Replace n with concatenation of its divisors. 53

%I

%S 1,12,13,124,15,1236,17,1248,139,12510,111,1234612,113,12714,13515,

%T 124816,117,1236918,119,12451020,13721,121122,123,1234681224,1525,

%U 121326,13927,12471428,129,12356101530,131,12481632,131133,121734,15735,123469121836,137

%N Replace n with concatenation of its divisors.

%C 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 a(n) is the concatenation of n-th row of the triangle in A027750.

%H R. Zumkeller, <a href="/A037278/b037278.txt">Table of n, a(n) for n = 1..10000</a>

%p a:=n->parse(cat(op(sort([op(divisors(n))])))):

%p seq(a(n),n=1..34); # _Paolo P. Lava_, Mar 29 2018

%t a[n_] := ToExpression[ StringJoin[ ToString /@ Divisors[n] ] ]; Table[ a[n], {n, 1, 34}] (* _Jean-François Alcover_, Dec 01 2011 *)

%t FromDigits[Flatten[IntegerDigits/@Divisors[#]]]&/@Range[40] (* _Harvey P. Dale_, Nov 09 2012 *)

%o (Haskell)

%o a037278 = read . concatMap show . a027750_row :: Integer -> Integer

%o -- _Reinhard Zumkeller_, Jul 13 2013, May 01 2012, Aug 07 2011

%o (PARI) a(n) = my(d=divisors(n), s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ _Michel Marcus_, Jun 01 2019

%o (MAGMA) k:=1; sol:=[];

%o for u in [1..34] do D:=Divisors(u); conc:=D[1];

%o for u1 in [2..#D] do a:=#Intseq(conc); a1:=#Intseq(D[u1]); conc:=10^a1*conc+D[u1];end for;

%o sol[u]:=conc; k:=k+1;

%o end for;

%o sol; // _Marius A. Burtea_, Jun 01 2019

%o (MATLAB) m=1;

%o for u=1:34 div=divisors(u); conc=str2num(strrep(num2str(div), ' ', ''));

%o sol(m)=conc; m=m+1;

%o end

%o sol % _Marius A. Burtea_, Jun 01 2019

%o (Python)

%o from sympy import divisors

%o def a(n): return int("".join(str(d) for d in divisors(n)))

%o print([a(n) for n in range(1, 35)]) # _Michael S. Branicky_, Dec 31 2020

%Y Cf. A027750, A037283, A037277, A106708.

%K nonn,easy,base,nice

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Erich Friedman_

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Last modified February 24 12:52 EST 2021. Contains 341569 sequences. (Running on oeis4.)