A344456 Composite numbers k such that (k-1) divides (A018804(k)-1).

41124, 230867, 358267, 37539572, 148025049, 235167249, 242788284, 1085464188, 142772845653, 202728626748

Offset: 1

Author

Max Alekseyev, May 19 2021

Keywords

• nonn
• hard
• more

Comments

For any prime p, (p-1) divides (A018804(p)-1) = 2(p-1).

Some larger terms: 62763888399737.

Links

• Pruthviraj et al., Are there infinitely many composite a such that Sum_{k=1..a} (k,a) == 1 (mod a-1)?, MathOverflow, 2021.

Crossrefs

Cf. A018804.

Programs

Mathematica

f[p_, e_] := (e*(p - 1)/p + 1)*p^e; pil[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[2, 400000], CompositeQ[#] && Divisible[pil[#] - 1, # - 1] &] (* Amiram Eldar, May 19 2021 *)

Extensions

a(9)-a(10) confirmed by Martin Ehrenstein, May 27 2021