A329461 Poulet numbers (Fermat pseudoprimes to base 2) k, whose sum of proper divisors sigma(k)-k is also a Poulet number.

513629, 3898129, 42656440661, 44368051087, 281257598737, 1746990146513, 5179966705541, 6275022424667, 9980519428181, 28343625432959, 37300616980817, 38107619098709, 55964206116901, 73114593538031, 123729699419917, 161656112395553, 297792380089151, 404770747208591

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