A359070
Smallest k > 1 such that k^n - 1 is the product of n distinct primes.
Original entry on oeis.org
3, 4, 15, 12, 39, 54, 79, 86, 144, 318, 1591, 144, 20131, 2014, 1764, 1308, 46656, 1296
Offset: 1
a(3) = 15 since 15^3 - 1 = 3374 = 2*7*241 is the product of 3 distinct primes and 15 is the smallest number with this property.
-
isok(k, n) = my(f=factor(k^n - 1)); issquarefree(f) && (omega(f) == n);
a(n) = my(k=2); while (!isok(k, n), k++); k; \\ Michel Marcus, Dec 15 2022
A379450
a(n) is the smallest prime p such that omega(p^n - 1) is equal to n, where omega = A001221.
Original entry on oeis.org
3, 5, 7, 11, 31, 11, 79, 47, 211, 113, 2473, 47, 45841, 389, 1123, 1061
Offset: 1
a(1) = 3 because omega(3^1 - 1) = omega(2) = 1,
a(2) = 5 because omega(5^2 - 1) = omega(24) = 2,
a(3) = 7 because omega(7^3 - 1) = omega(342) = 3.
-
a[n_] := Module[{p = 2}, While[PrimeNu[p^n - 1] != n, p = NextPrime[p]]; p]; Array[a, 12] (* Amiram Eldar, Dec 25 2024 *)
-
a(n) = my(p=2); while (omega(p^n - 1) != n, p=nextprime(p+1)); p; \\ Michel Marcus, Dec 24 2024
A368163
a(n) is the smallest number k > 1 such that bigomega(k^n - 1) = n.
Original entry on oeis.org
3, 4, 4, 10, 17, 8, 25, 5, 28, 9, 81, 13, 289, 64, 100, 41, 6561, 31, 6657, 57, 529, 1025
Offset: 1
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.
Showing 1-3 of 3 results.
Comments