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A161901 Array read by rows in which row n lists the divisors of n, but if n is a square then the square root of n appears twice.

%I A161901 #13 Sep 27 2020 13:38:46
%S A161901 1,1,1,2,1,3,1,2,2,4,1,5,1,2,3,6,1,7,1,2,4,8,1,3,3,9,1,2,5,10,1,11,1,
%T A161901 2,3,4,6,12,1,13,1,2,7,14,1,3,5,15,1,2,4,4,8,16,1,17,1,2,3,6,9,18,1,
%U A161901 19,1,2,4,5,10,20,1,3,7,21
%N A161901 Array read by rows in which row n lists the divisors of n, but if n is a square then the square root of n appears twice.
%C A161901 Row n has length A161841(n). Row sums give A060866. - _Omar E. Pol_, Jan 06 2014
%H A161901 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>
%H A161901 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polprdipi.jpg">Illustration: Divisors and pi(x)</a>
%e A161901 Array begins:
%e A161901 ....... 1,1;
%e A161901 ....... 1,2;
%e A161901 ....... 1,3;
%e A161901 ..... 1,2,2,4;
%e A161901 ....... 1,5;
%e A161901 ..... 1,2,3,6;
%e A161901 ....... 1,7;
%e A161901 ..... 1,2,4,8;
%e A161901 ..... 1,3,3,9;
%e A161901 ..... 1,2,5,10;
%e A161901 ....... 1,11;
%e A161901 ... 1,2,3,4,6,12;
%e A161901 ....... 1,13;
%e A161901 ..... 1,2,7,14;
%e A161901 ..... 1,3,5,15;
%e A161901 ... 1,2,4,4,8,16;
%t A161901 dsr[n_]:=If[IntegerQ[Sqrt[n]],Sort[Join[{Sqrt[n]},Divisors[n]]],Divisors[ n]]; Array[ dsr,30]//Flatten (* _Harvey P. Dale_, Sep 27 2020 *)
%Y A161901 Cf. A000005, A027750, A038548, A161841, A161842.
%K A161901 easy,nonn,tabf
%O A161901 1,4
%A A161901 _Omar E. Pol_, Jun 23 2009
%E A161901 Keyword tabf added by _R. J. Mathar_, Jun 28 2009
%E A161901 Definition clarified by _Harvey P. Dale_, Sep 27 2020