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.

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, 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, 19, 1, 2, 4, 5, 10, 20, 1, 3, 7, 21

Offset: 1

Author

Omar E. Pol, Jun 23 2009

Keywords

• easy
• nonn
• tabf

Comments

Row n has length A161841(n). Row sums give A060866. - Omar E. Pol, Jan 06 2014

Examples

			Array begins:
....... 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;
... 1,2,3,4,6,12;
....... 1,13;
..... 1,2,7,14;
..... 1,3,5,15;
... 1,2,4,4,8,16;
		

Links

• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos
• Omar E. Pol, Illustration: Divisors and pi(x)

Crossrefs

Cf. A000005, A027750, A038548, A161841, A161842.

Programs

Mathematica

dsr[n_]:=If[IntegerQ[Sqrt[n]],Sort[Join[{Sqrt[n]},Divisors[n]]],Divisors[ n]]; Array[ dsr,30]//Flatten (* Harvey P. Dale, Sep 27 2020 *)

Extensions

Keyword tabf added by R. J. Mathar, Jun 28 2009

Definition clarified by Harvey P. Dale, Sep 27 2020