A389150 Nonprimes k with no proper divisor d such that gcd(d^2 - 1, k) = 1.

1, 6, 30, 42, 870, 930, 1722, 1806, 863970, 2963562, 2967006

Offset

1,2

Comments

Is this sequence finite or infinite? It contains 6, 30, 42, 1722, .., which are members of another known sequence A014574. A second question is also interesting: is their number finite or infinite?

a(12) > 10^9 if it exists. - Robert Israel, Oct 01 2025

All terms are squarefree, and all except 1 are divisible by 6. - Robert Israel, Oct 01 2025

Links

Table of n, a(n) for n=1..11.

Maple

filter:= proc(k)
  if isprime(k) then return false fi;
  andmap(d -> igcd(k, d^2-1) <> 1, numtheory:-divisors(k) minus {k})
end proc:
select(filter, [$1..3*10^6]); # Robert Israel, Sep 25 2025

Mathematica

Join[{1}, Select[Range[6, 3*10^6, 6], MoebiusMu[#] != 0 && With[{k = #}, NoneTrue[Divisors[k][[2 ;; -2]], CoprimeQ[#^2 - 1, k] &]] &]] (* Paolo Xausa, Oct 01 2025 *)

Prog

(Magma) [k: k in [1..10^6] | not IsPrime(k) and #[d: d in Divisors(k) | Gcd(d^2-1, k) eq 1] eq 1];
(PARI) isok(k) = !isprime(k) && sumdiv(k, d, gcd(d^2 - 1, k)==1) == 1; \\ Michel Marcus, Sep 25 2025

Crossrefs

Cf. A000005, A000010, A014574.

Sequence in context: A326580 A070195 A241190 * A276933 A110175 A249676

Adjacent sequences: A389147 A389148 A389149 * A389151 A389152 A389153

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Sep 25 2025

Status

approved