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A277285 Numbers n such that d(n) divides 2^n-1. 2
1, 4, 16, 36, 144, 324, 400, 576, 729, 784, 900, 1764, 1936, 2304, 2500, 2704, 2916, 3600, 4356, 4624, 5184, 5776, 6084, 7056, 8100, 8464, 9604, 10000, 10404, 11664, 12996, 13456, 14400, 15376, 15876, 16384, 17424, 19044, 20736, 21904, 22500, 24336, 25600, 26244, 26896, 28224, 29584, 30276 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence is infinite and all terms are squares. Square roots of terms are 1, 2, 4, 6, 12, 18, 20, 24, 27, 28, 30, 42, 44, 48, 50, 52, 54, 60, 66, 68, 72, 76, 78, 84, 90, 92, 98, 100, 102, 108, 114, 116, 120, 124, 126, 128, 132, 138, 144, ...

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

MAPLE

a:= proc(n) option remember; local k;

      for k from 1+`if`(n=1, 0, a(n-1))

      while 0<>2&^k-1 mod numtheory[tau](k) do od; k

    end:

seq(a(n), n=1..50);  # Alois P. Heinz, Nov 06 2016

MATHEMATICA

Select[Range[10^5], Divisible[2^# - 1, DivisorSigma[0, #]] &] (* Michael De Vlieger, Oct 10 2016 *)

PROG

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

(PARI) is(n)=Mod(2, numdiv(n))^n==1; \\ Joerg Arndt, Oct 09 2016

(Python)

from sympy import divisor_count

A277285_list = [1] + [j for j in (i**2 for i in range(1, 10**4)) if pow(2, j, int(divisor_count(j))) == 1] # Chai Wah Wu, Nov 06 2016

CROSSREFS

Cf. A000005, A000225, A277185.

Sequence in context: A318149 A233409 A181795 * A136404 A176471 A046952

Adjacent sequences:  A277282 A277283 A277284 * A277286 A277287 A277288

KEYWORD

nonn

AUTHOR

Altug Alkan, Oct 09 2016, following a suggestion from Michel Marcus and N. J. A. Sloane

STATUS

approved

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Last modified May 16 09:28 EDT 2021. Contains 343940 sequences. (Running on oeis4.)