A276238 -id:A276238 - cp's OEIS frontend

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

Joseph L. Pe, Jan 30 2014

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

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

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.

Supersequence of A015715.

Cf. A000203, A051179, A020492, A276238.

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

s=[1]; for(n=1, 10000, if(2^sigma(n)%n==1, s=concat(s, n))); s \\ Colin Barker, Jan 30 2014

isok(n) = Mod(2, n)^sigma(n)==1; \\ Altug Alkan, Sep 19 2017

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

A291164 Numbers k such that 2^psi(k) == -1 (mod k) where psi(k) = A001615(k).

Original entry on oeis.org

1, 5, 25, 125, 625, 3125, 4097, 7361, 15625, 69649, 78125, 85073, 125137, 390625, 658529, 987377, 1184033, 1953125, 2127329, 2358529, 3187313, 3999137, 9765625, 11194993, 16777217, 16785409, 20128561, 20502593, 30030769, 36164593, 40094993, 48828125, 50281793

Offset: 1

Altug Alkan, Aug 19 2017

nonn

			7361 is a term because 7361 = 17*433 divides 2^psi(7361) + 1 = 2^(18*434) + 1.

Cf. A001615, A276238.

a001615(n) = n*sumdivmult(n, d, issquarefree(d)/d);
is(n) = Mod(2,n)^a001615(n)==-1;

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

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A291164 Numbers k such that 2^psi(k) == -1 (mod k) where psi(k) = A001615(k).

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