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

1,4

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

Formula

a(n) = denominator((2^n - 2)/n). - 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 *)

Prog

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

Crossrefs

Cf. A000918, A146077.

Sequence in context: A326139 A325641 A325563 * A032742 A060654 A291329

Adjacent sequences: A159350 A159351 A159352 * A159354 A159355 A159356

Keyword

nonn

Author

Leroy Quet, Apr 11 2009

Extensions

Extended by Ray Chandler, Apr 11 2009

Status

approved