A277185 Odd numbers n such that d(n) divides 2^n-1.

1, 729, 85766121, 1340095640625, 151939915084881, 413976684737889, 2070185663499849, 4034942722397601, 12696463968316569

Offset

1,2

Comments

Subsequence of odd terms of A277285.

Sequence is infinite. In particular, n = (21p)^6 for primes p = 5 or p > 7 are such: d(n) = 7^3 divides 2^147 - 1, which in turn divides 2^n - 1. - Max Alekseyev, 30 Sep 2016

Note that there are also other forms. For example, (A002110(6)/2)^6 is a term.

Links

Table of n, a(n) for n=1..9.

Example

Odd number 729 is a term because 2^729-1 is divisible by d(729) = 7.

Mathematica

Select[Range[1000], Mod[ 2^# - 1, DivisorSigma[0, # ]] == 0 && OddQ[#] &] (* G. C. Greubel, Oct 18 2016 *)

Prog

(PARI) is(n) = (2^n-1) % numdiv(n) == 0 && n % 2 == 1;

Crossrefs

Cf. A000005, A000225, A277285.

Sequence in context: A017430 A017562 A013852 * A343693 A357960 A352034

Adjacent sequences: A277182 A277183 A277184 * A277186 A277187 A277188

Keyword

nonn,more

Author

Altug Alkan, Oct 03 2016

Extensions

a(4)-a(9) from Giovanni Resta, Oct 03 2016

Status

approved