A056926 - OEIS

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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

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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.