A159353 a(n) = the smallest positive integer such that a(n)*(2^n - 2) is a multiple of n.

1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 1, 10, 7, 11, 1, 12, 5, 13, 9, 2, 1, 15, 1, 16, 11, 17, 35, 18, 1, 19, 13, 20, 1, 21, 1, 22, 3, 23, 1, 24, 7, 25, 17, 26, 1, 27, 55, 28, 19, 29, 1, 30, 1, 31, 21, 32, 13, 33, 1, 34, 23, 5, 1, 36, 1, 37, 25, 38, 77, 39, 1, 40, 27, 41, 1, 42

Offset: 1

Author

Leroy Quet, Apr 11 2009

Keywords

• nonn

Comments

This is not the same as sequence A032742, where A032742(n) = the largest proper divisor of n. See A146077 for indices at which A032742 and this sequence differ.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000918, A146077.

Programs

Magma

[Denominator((2^n-2)/n): n in [1..84]]; // Juri-Stepan Gerasimov, Sep 09 2014

Mathematica

Array[Block[{k = 1}, While[! Divisible[k (2^# - 2), #], k++]; k] &, 84] (* Michael De Vlieger, Oct 30 2017 *)

PARI

a(n)=my(k=1);while((2^n-2)*k%n != 0,k++);return(k) \\ Edward Jiang, Sep 09 2014

PARI

a(n)=denominator(lift(Mod(2,n)^n-2)/n) \\ Charles R Greathouse IV, Sep 11 2014

Formula

a(n) = denominator((2^n - 2)/n). - Juri-Stepan Gerasimov, Sep 09 2014

Extensions

Extended by Ray Chandler, Apr 11 2009