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

1,4

Comments

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

Links

Table of n, a(n) for n=1..74.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos

Omar E. Pol, Illustration: Divisors and pi(x)

Example

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;

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 *)

Crossrefs

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

Sequence in context: A339443 A369323 A342655 * A102862 A029331 A037269

Adjacent sequences: A161898 A161899 A161900 * A161902 A161903 A161904

Keyword

easy,nonn,tabf

Author

Omar E. Pol, Jun 23 2009

Extensions

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

Definition clarified by Harvey P. Dale, Sep 27 2020

Status

approved