A329203 Numbers k such that A329308(k) = 0.

1, 2, 3, 4, 5, 8, 9, 13, 17, 24, 33, 40, 64, 76, 108, 116, 208, 220, 324, 496, 504, 564, 1176

Offset

1,2

Comments

Numbers k such that there is no m < sqrt(k) for which k mod (m^2) is prime.

No more terms up to 2*10^7. I conjecture that these are all the terms.

Links

Table of n, a(n) for n=1..23.

Example

a(7) = 17 is in the sequence because 17 mod (2^2) = 1, 17 mod (3^2) = 8 and 17 mod (4^2) = 1 are all nonprime while 5^2 > 17.
20 is not in the sequence because 20 mod (3^2) = 2 is prime and 3^2 < 20.

Maple

filter:= proc(n) local k;
  for k from 2 to floor(sqrt(n)) do if isprime(n mod k^2) then return false fi od:
  true
end proc:
select(filter, [$1..10^6]);

Prog

(Magma) [m:m in [1..2000]| #[k:k in [2..Floor(Sqrt(m))]| IsPrime(m mod k^2) ] eq 0]; // Marius A. Burtea, Nov 11 2019

Crossrefs

Cf. A329308.

Sequence in context: A349412 A317082 A268359 * A054181 A329563 A163077

Adjacent sequences: A329200 A329201 A329202 * A329204 A329205 A329206

Keyword

nonn,more

Author

Robert Israel, Nov 10 2019

Status

approved