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

0,5

Comments

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

Links

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000196, A037213.

Sequence in context: A260089 A296240 A158464 * A137773 A175010 A107454

Adjacent sequences: A056923 A056924 A056925 * A056927 A056928 A056929

Keyword

easy,nonn

Author

Henry Bottomley, Jul 12 2000

Extensions

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

Status

approved