A300327 - OEIS

%I #19 Mar 06 2023 07:21:21

%S 341,13981,126217,294409,2113665,4670029,127479097,140996401,

%T 509033161,8600780461,42625846021,220411358713,2382784226641,

%U 11361630988981,56308742593741,431283945022021,434124350060401,2056455209005561,5598600634063801,8178192276975721

%N Poulet numbers (Fermat pseudoprimes to base 2) with a record number of divisors that are also Poulet numbers.

%C The number of divisors is 1, 2, 3, 4, 5, 6, 7, 8, 13, 15, 16, 20, 23, ...

%H Daniel Suteu, <a href="/A300327/b300327.txt">Table of n, a(n) for n = 1..25</a>

%H Jan Feitsma and William F. Galway, <a href="http://www.cecm.sfu.ca/Pseudoprimes/index-2-to-64.html">Tables of pseudoprimes and related data</a>.

%H R. G. E. Pinch, <a href="http://s369624816.websitehome.co.uk/rgep/psp-13.gz">Pseudoprimes up to 10^13</a>.

%e 294409 is in the sequence since it is a Poulet number, and 4 of its divisors are also Poulet numbers (2701, 4033, 7957, 294409), more than for any smaller Poulet number.

%o (PARI) isP(n) = {Mod(2, n)^n==2 & !isprime(n) & n>1};

%o lista(nn) = {rec = 0; for (n=1, nn, if (isP(n), nb = sumdiv(n, d, isP(d)); if (nb > rec, print1(n, ", "); rec = nb);););} \\ _Michel Marcus_, Mar 07 2018

%Y Cf. A001567, A290497.

%K nonn

%O 1,1

%A _Amiram Eldar_, Mar 03 2018

%E a(14)-a(20) from _Daniel Suteu_, Mar 06 2023