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Poulet numbers (Fermat pseudoprimes to base 2) k, whose sum of proper divisors sigma(k)-k is also a Poulet number.
1

%I #9 Nov 16 2019 10:52:19

%S 513629,3898129,42656440661,44368051087,281257598737,1746990146513,

%T 5179966705541,6275022424667,9980519428181,28343625432959,

%U 37300616980817,38107619098709,55964206116901,73114593538031,123729699419917,161656112395553,297792380089151,404770747208591

%N Poulet numbers (Fermat pseudoprimes to base 2) k, whose sum of proper divisors sigma(k)-k is also a Poulet number.

%C The corresponding sums of proper divisors are 2047, 4371, 476971, 526593, 1325843, 5919187, 5256091, 6631549, 7295851, 18007345, 31166803, 17641207, 10274913907, 73562833, 27808463, 68512867, 48269761, 75501793, ...

%C There are 72 terms below 2^64, 71 of them have 2 prime factors, and only one has 3 prime factors: 55964206116901 = 6361 * 47701 * 184441.

%H Amiram Eldar, <a href="/A329461/b329461.txt">Table of n, a(n) for n = 1..72</a>

%e 513629 is a Poulet number, and sigma(513629)-513629 = 2047 is also a Poulet number.

%t pouletQ[n_] := CompositeQ[n ]&& PowerMod[2, n - 1, n] == 1; s[n_] := DivisorSigma[ 1, n] - n; seq={}; Do[If[pouletQ[n] && pouletQ[s[n]], AppendTo[seq, n]], {n,1,10^7}]; seq

%Y Cf. A001065, A001567.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 13 2019