A056926 a(n) = sqrt(n) if n is a square, otherwise 1.

0, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1

Offset: 0

Author

Henry Bottomley, Jul 12 2000

Keywords

• easy
• nonn

Comments

Like A037213, but has 1's instead of 0's for nonsquare n > 0. - Antti Karttunen, Jul 22 2018

Examples

			a(24) = 1 because 24 is not a square, a(25) = 5 because 25 = 5^2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A000196, A037213.

Programs

Mathematica

sq1[n_]:=Module[{sn=Sqrt[n]},If[IntegerQ[sn],sn,1]]; Array[sq1,110] (* Harvey P. Dale, Jul 25 2011 *)

PARI

A056926(n) = if(issquare(n,&n),n,1); \\ Antti Karttunen, Jul 22 2018

Formula

a(n) = A007955(n)/A056925(n) = 1 + (sqrt(n)-1)*A010052(n), for all n >= 1.

a(n) = n^((d(n) mod 2)/2) for n>=1. - Wesley Ivan Hurt, Jun 07 2023

Extensions

Term a(0) = 0 prepended by Antti Karttunen, Jul 22 2018