A300327 Poulet numbers (Fermat pseudoprimes to base 2) with a record number of divisors that are also Poulet numbers.

341, 13981, 126217, 294409, 2113665, 4670029, 127479097, 140996401, 509033161, 8600780461, 42625846021, 220411358713, 2382784226641, 11361630988981, 56308742593741, 431283945022021, 434124350060401, 2056455209005561, 5598600634063801, 8178192276975721

Offset

1,1

Comments

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

Links

Daniel Suteu, Table of n, a(n) for n = 1..25

Jan Feitsma and William F. Galway, Tables of pseudoprimes and related data.

R. G. E. Pinch, Pseudoprimes up to 10^13.

Example

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.

Prog

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

Crossrefs

Cf. A001567, A290497.

Sequence in context: A069309 A353021 A086806 * A289305 A309285 A317556

Adjacent sequences: A300324 A300325 A300326 * A300328 A300329 A300330

Keyword

nonn

Author

Amiram Eldar, Mar 03 2018

Extensions

a(14)-a(20) from Daniel Suteu, Mar 06 2023

Status

approved