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

Author

Joseph L. Pe, Jan 30 2014

Keywords

• nonn
• easy

Comments

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

Examples

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

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.

Crossrefs

Supersequence of A015715.

Cf. A000203, A051179, A020492, A276238.

Programs

Mathematica

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

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

Extensions

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