A368163 a(n) is the smallest number k > 1 such that bigomega(k^n - 1) = n.

3, 4, 4, 10, 17, 8, 25, 5, 28, 9, 81, 13, 289, 64, 100, 41, 6561, 31, 6657, 57, 529, 1025

Offset: 1

Author

Daniel Suteu, Dec 14 2023

Keywords

• nonn
• more
• hard

Comments

a(23) <= 196609; a(24) = 79; a(25) <= 28561; a(26) = 14015; a(27) = 961; a(28) = 729; a(30) = 361; a(32) = 2047.

Examples

			a(5) = 17 is the smallest number of the set {k(i)} = {17, 19, 21, 26, 27, 39, 45, ...} where k(i)^5 - 1 has exactly 5 prime factors counted with multiplicity.
		

Crossrefs

Cf. A001222, A219019, A241793, A359070.

Programs

PARI

a(n) = my(k=2); while (bigomega(k^n-1) != n, k++); k;