A236693 - OEIS

%I #24 Mar 13 2020 08:36:30

%S 1,3,15,35,51,65,105,119,195,255,315,323,357,377,455,459,585,595,663,

%T 969,1045,1071,1105,1131,1189,1365,1455,1469,1485,1547,1615,1785,1799,

%U 1885,1887,1911,2261,2295,2385,2639,2795,2907,3135,3145,3185,3213,3315,3339

%N Numbers k such that 2^sigma(k) == 1 (mod k).

%C This sequence is infinite since A051179(n) is a term. - _Jinyuan Wang_, Mar 13 2020

%H Jinyuan Wang, <a href="/A236693/b236693.txt">Table of n, a(n) for n = 1..10000</a>

%H Florian Luca, <a href="https://eudml.org/doc/125862">Positive integers n such that n| a^sigma(n) - 1</a>, Novi Sad Journal of Mathematics, Vol 33, No. 2 (2003), pp. 49-66.

%e 2^sigma(15) = 2^24 = 16777216 is congruent to 1 (mod 15), so 15 is a term of the sequence.

%t l = {1};

%t For[i = 1, i <= 10^4, i++,

%t     If[Mod[2^DivisorSigma[1, i], i] == 1, l = Append[l, i]]];

%t l

%o (PARI) s=[1]; for(n=1, 10000, if(2^sigma(n)%n==1, s=concat(s, n))); s \\ _Colin Barker_, Jan 30 2014

%o (PARI) isok(n) = Mod(2, n)^sigma(n)==1; \\ _Altug Alkan_, Sep 19 2017

%Y Supersequence of A015715.

%Y Cf. A000203, A051179, A020492, A276238.

%K nonn,easy

%O 1,2

%A _Joseph L. Pe_, Jan 30 2014

%E a(1) = 1 added by _Amiram Eldar_, Sep 19 2017