A385315 Smallest number k such that both k^n - 1 and k^n + 1 have n prime factors, counted with repetitions.

4, 12, 66, 920, 26, 132, 79, 17958, 53, 693, 4181, 122160, 29791, 32318, 971

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Jean-Marc Rebert, Factorizations of k^n-1 and k^n+1

Formula

a(n) >= max(A368162(n), A368163(n)). - Daniel Suteu, Sep 02 2025

Example

a(1) = 4, because 4^1 - 1 = 3 and 4^1 + 1 = 5, and no lesser number has this property.
See the Links section for more examples.

Prog

(PARI) a(n) = my(k=2, kn=k^n); while ((bigomega(kn-1)!=n) || (bigomega(kn+1)!=n), k++; kn=k^n); k; \\ Michel Marcus, Aug 18 2025

Crossrefs

Cf. A001222, A001358, A014612, A078840, A385591, A368162, A368163.

Sequence in context: A339134 A000843 A369284 * A358409 A180386 A302434

Adjacent sequences: A385312 A385313 A385314 * A385316 A385317 A385318

Keyword

nonn,more,hard

Author

Jean-Marc Rebert, Aug 12 2025

Status

approved