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A379768 a(n) is the smallest prime p such that omega(p^n + 1) = n.

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%I A379768 #17 Jan 12 2025 09:14:45
%S A379768 2,3,5,43,17,47,151,1697,59,2153,521,13183,30089,66569,761
%N A379768 a(n) is the smallest prime p such that omega(p^n + 1) = n.
%C A379768 2*10^6 < a(16) <= 206874667; a(18) = 33577; a(20) <= 3258569.
%C A379768 A219018(n) <= a(n) <= A280005(n).
%e A379768 a(3) = 5 is the smallest prime of the set {p(i)} = {5, 11, 13, 19, 23, ...} where omega(p(i)^3 + 1) = 3.
%t A379768 a[n_] := Module[{p = 2}, While[PrimeNu[p^n + 1] != n, p = NextPrime[p]]; p]; Print[Array[a, 11]]
%o A379768 (PARI) a(n) = forprime(p=2, oo, if(omega(p^n+1) == n, return(p)));
%Y A379768 Cf. A001221, A219018, A242786, A280005, A362957, A379450.
%K A379768 nonn,more,hard
%O A379768 1,1
%A A379768 _Daniel Suteu_, Jan 06 2025