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 A329461 Poulet numbers (Fermat pseudoprimes to base 2) k, whose sum of proper divisors sigma(k)-k is also a Poulet number. 1
 513629, 3898129, 42656440661, 44368051087, 281257598737, 1746990146513, 5179966705541, 6275022424667, 9980519428181, 28343625432959, 37300616980817, 38107619098709, 55964206116901, 73114593538031, 123729699419917, 161656112395553, 297792380089151, 404770747208591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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, ... 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. LINKS Amiram Eldar, Table of n, a(n) for n = 1..72 EXAMPLE 513629 is a Poulet number, and sigma(513629)-513629 = 2047 is also a Poulet number. MATHEMATICA 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 CROSSREFS Cf. A001065, A001567. Sequence in context: A233858 A306952 A336060 * A257424 A257431 A254240 Adjacent sequences:  A329458 A329459 A329460 * A329462 A329463 A329464 KEYWORD nonn AUTHOR Amiram Eldar, Nov 13 2019 STATUS approved

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Last modified August 14 13:57 EDT 2020. Contains 336481 sequences. (Running on oeis4.)