A236693 Numbers k such that 2^sigma(k) == 1 (mod k).

1, 3, 15, 35, 51, 65, 105, 119, 195, 255, 315, 323, 357, 377, 455, 459, 585, 595, 663, 969, 1045, 1071, 1105, 1131, 1189, 1365, 1455, 1469, 1485, 1547, 1615, 1785, 1799, 1885, 1887, 1911, 2261, 2295, 2385, 2639, 2795, 2907, 3135, 3145, 3185, 3213, 3315, 3339

Offset

1,2

Comments

This sequence is infinite since A051179(n) is a term. - Jinyuan Wang, Mar 13 2020

Links

Jinyuan Wang, Table of n, a(n) for n = 1..10000

Florian Luca, Positive integers n such that n| a^sigma(n) - 1, Novi Sad Journal of Mathematics, Vol 33, No. 2 (2003), pp. 49-66.

Example

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

Mathematica

l = {1};
For[i = 1, i <= 10^4, i++,
    If[Mod[2^DivisorSigma[1, i], i] == 1, l = Append[l, i]]];
l

Prog

(PARI) s=[1]; for(n=1, 10000, if(2^sigma(n)%n==1, s=concat(s, n))); s \\ Colin Barker, Jan 30 2014
(PARI) isok(n) = Mod(2, n)^sigma(n)==1; \\ Altug Alkan, Sep 19 2017

Crossrefs

Supersequence of A015715.

Cf. A000203, A051179, A020492, A276238.

Sequence in context: A331249 A102790 A317182 * A317183 A000466 A241237

Adjacent sequences: A236690 A236691 A236692 * A236694 A236695 A236696

Keyword

nonn,easy

Author

Joseph L. Pe, Jan 30 2014

Extensions

a(1) = 1 added by Amiram Eldar, Sep 19 2017

Status

approved