A241793
Least number k such that k^n and k^n-1 contain the same number of prime factors (counted with multiplicity) or 0 if no such k exists.
Original entry on oeis.org
3, 34, 5, 15, 17, 55, 79, 5, 53, 23, 337, 13, 601, 79, 241, 41, 18433, 31, 40961, 89, 3313, 1153
Offset: 1
2^1 (2) and 2^1-1 (1) do not have the same number of prime factors. 3^1 (3) and 3^1-1 (2) have the same number of prime factors. Thus a(1) = 3.
A368162
a(n) is the smallest number k > 0 such that bigomega(k^n + 1) = n.
Original entry on oeis.org
1, 3, 3, 43, 7, 32, 23, 643, 17, 207, 251, 3255, 255, 1568, 107
Offset: 1
a(5) = 7 is the smallest number of the set {k(i)} = {7, 14, 24, 26, 46, 51, ...} where k(i)^5 + 1 has exactly 5 prime factors counted with multiplicity.
A379768
a(n) is the smallest prime p such that omega(p^n + 1) = n.
Original entry on oeis.org
2, 3, 5, 43, 17, 47, 151, 1697, 59, 2153, 521, 13183, 30089, 66569, 761
Offset: 1
a(3) = 5 is the smallest prime of the set {p(i)} = {5, 11, 13, 19, 23, ...} where omega(p(i)^3 + 1) = 3.
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a[n_] := Module[{p = 2}, While[PrimeNu[p^n + 1] != n, p = NextPrime[p]]; p]; Print[Array[a, 11]]
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a(n) = forprime(p=2, oo, if(omega(p^n+1) == n, return(p)));
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