A075106 -id:A075106 - cp's OEIS frontend

A075105 Numerator of n/floor(log_2(n)); denominator is A075106(n).

2, 3, 2, 5, 3, 7, 8, 3, 10, 11, 4, 13, 14, 5, 4, 17, 9, 19, 5, 21, 11, 23, 6, 25, 13, 27, 7, 29, 15, 31, 32, 33, 34, 7, 36, 37, 38, 39, 8, 41, 42, 43, 44, 9, 46, 47, 48, 49, 10, 51, 52, 53, 54, 11, 56, 57, 58, 59, 12, 61, 62, 63, 32, 65, 11, 67, 34, 23, 35, 71, 12, 73, 37, 25, 38

Offset: 2

Reinhard Zumkeller, Sep 02 2002

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Cf. A000523, A075104, A075106.

import Data.Ratio ((%), numerator)
a075105 n = numerator $ n % a000523 n
-- Reinhard Zumkeller, Jul 08 2014

Table[n/Floor[Log[2,n]],{n,2,80}]//Numerator (* Harvey P. Dale, Feb 25 2018 *)

a(n) = n/A075104(n).

A075104 Greatest common divisor of n and integer part of log_2(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 3, 1, 1, 3, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2

Offset: 1

Reinhard Zumkeller, Sep 02 2002

nonn

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

Cf. A000523, A075105, A075106.

a075104 n = gcd n $ a000523 n  -- Reinhard Zumkeller, Jul 08 2014

Table[GCD[n,IntegerPart[Log[2,n]]],{n,110}] (* Harvey P. Dale, Apr 21 2016 *)

a(n) = gcd(n, A000523(n)).

A075107 Number of steps to reach the first integer (= A075108(n)) starting with n/floor(log_2(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, 2, 0, 1, 1, 0, 5, 2, 0, 3, 2, 0, 0, 3, 3, 2, 0, 2, 1, 3, 0, 2, 2, 2, 0, 1, 1, 1, 2, 5, 3, 0, 16, 2, 4, 6, 0, 4, 16, 9, 2, 0, 1, 1, 1, 1, 0, 4, 2, 4, 8, 0, 2, 5, 2, 8, 0, 9, 3, 4, 5, 2, 0, 1, 1, 1, 1, 1, 0, 5, 7, 3, 2, 4, 0, 9, 4, 1, 2, 3, 0, 4, 1, 2, 1

Offset: 2

Reinhard Zumkeller, Sep 02 2002

nonn

Starting values given by A075105(n)/A075106(n).

			a(5)=2 since 5/floor(log_2(5)) = 5/2 -> 15/2 -> 60 = A075108(5).

Cf. A068119, A073524, A075102, A075120.

More terms from Jinyuan Wang, Jan 15 2022

cp's OEIS Frontend

A075105 Numerator of n/floor(log_2(n)); denominator is A075106(n).

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A075104 Greatest common divisor of n and integer part of log_2(n).

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Haskell

Mathematica

Formula

A075107 Number of steps to reach the first integer (= A075108(n)) starting with n/floor(log_2(n)) and iterating the map x -> x*ceiling(x), or -1 if no integer is ever reached.

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