A075119 -id:A075119 - cp's OEIS frontend

A073890 Numerator of n/floor(sqrt(n)).

1, 2, 3, 2, 5, 3, 7, 4, 3, 10, 11, 4, 13, 14, 5, 4, 17, 9, 19, 5, 21, 11, 23, 6, 5, 26, 27, 28, 29, 6, 31, 32, 33, 34, 7, 6, 37, 19, 13, 20, 41, 7, 43, 22, 15, 23, 47, 8, 7, 50, 51, 52, 53, 54, 55, 8, 57, 58, 59, 60, 61, 62, 9, 8, 65, 33, 67, 17, 69, 35, 71, 9, 73, 37, 75, 19, 77

Offset: 1

Reinhard Zumkeller, Sep 03 2002

Denominator is A075119(n).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000196, A067815, A075119 (denominator).

import Data.Ratio ((%), numerator)
a073890 n = numerator $ n % a000196 n
-- Reinhard Zumkeller, Jul 08 2014

a(n) = numerator(n/sqrtint(n)); \\ Michel Marcus, Dec 19 2017

a(n) = n/A067815(n).

Denominator reference fixed by Reinhard Zumkeller, Jul 08 2014

A067815 a(n) = gcd(n, floor(sqrt(n))).

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, Feb 08 2002

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000196, A073890, A075119.

a067815 n = gcd n $ a000196 n  -- Reinhard Zumkeller, Jul 08 2014

a[n_] := GCD[n, Floor[Sqrt[n]]]; Array[a, 100] (* Amiram Eldar, Nov 19 2024 *)

a(n) = gcd(n, sqrtint(n)); \\ Altug Alkan, Dec 19 2017

A075120 Number of steps to reach the first integer (= A075121(n)) starting with n/floor(sqrt(n)) and iterating the map x -> x*ceiling(x), or -1 if no integer is ever reached.

Original entry on oeis.org

0, 0, 0, 0, 2, 0, 1, 0, 0, 5, 2, 0, 3, 2, 0, 0, 3, 3, 2, 0, 2, 1, 3, 0, 0, 8, 3, 5, 2, 0, 3, 2, 5, 3, 0, 0, 6, 2, 2, 4, 2, 0, 5, 3, 1, 4, 2, 0, 0, 7, 12, 5, 11, 12, 2, 0, 4, 3, 9, 12, 6, 16, 0, 0, 3, 7, 8, 4, 4, 4, 2, 0, 2, 4, 5, 1, 5, 2, 5, 0, 0, 7, 3, 22, 3, 3

Offset: 1

Reinhard Zumkeller, Sep 03 2002

nonn

Starting with A073890(n)/A075119(n).

			a(13)=3 since 13/floor(sqrt(13)) = 13/3 -> 65/3 -> 1430/3 -> 227370 = A075121(13).

Cf. A068119, A073524, A075102, A075107, A075121.

More terms from Jinyuan Wang, Jan 15 2022

cp's OEIS Frontend

A073890 Numerator of n/floor(sqrt(n)).

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A067815 a(n) = gcd(n, floor(sqrt(n))).

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A075120 Number of steps to reach the first integer (= A075121(n)) starting with n/floor(sqrt(n)) and iterating the map x -> x*ceiling(x), or -1 if no integer is ever reached.

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