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A358881 a(n) is the smallest prime p such that p^2 - 1 has 2*n divisors, or -1 if no such prime exists.

%I A358881 #22 Feb 16 2025 17:52:36
%S A358881 2,3,-1,5,7,-1,-1,11,17,23,-1,19,-1,31,73,29,-1,383,-1,41,97,-1,-1,79,
%T A358881 -1,-1,127,223,-1,71,-1,109,-1,-1,2593,197,-1,-1,-1,281,-1,1439,-1,
%U A358881 34303,199,-1,-1,181,-1,647,-1,6143,-1,7057,-1,929,-1,-1,-1,521,-1
%N A358881 a(n) is the smallest prime p such that p^2 - 1 has 2*n divisors, or -1 if no such prime exists.
%C A358881 See A350780 for a discussion about the prime solution to d(p^2 - 1) = 2*n for n in certain cases. - _Jianing Song_, Feb 15 2025
%H A358881 Jianing Song, <a href="/A358881/b358881.txt">Table of n, a(n) for n = 1..374</a>
%H A358881 Jianing Song, <a href="/A350780/a350780.pdf">Notes on A350780 and A358881 (1)</a>
%H A358881 Jianing Song, <a href="/A350780/a350780_1.pdf">Notes on A350780 and A358881 (2)</a>
%H A358881 Jianing Song, <a href="/A350780/a350780_1.txt">PARI program for A350780 and A358881</a>
%e A358881 For p = 11, p^2 - 1 = 121 - 1 = 120 = 2^3 * 3 * 5 has 16 divisors. 11 is the smallest prime p such that p^2 - 1 has 16 = 2*8 divisors, so a(8) = 11.
%e A358881 There does not exist any prime p such that p^2 - 1 has 6 = 2*3 divisors, so a(3) = -1.
%o A358881 (PARI) \\ See Links. _Jianing Song_, Feb 16 2025
%Y A358881 Cf. A000005, A000040, A341655, A341658, A341660, A350780.
%K A358881 sign,hard
%O A358881 1,1
%A A358881 _Jon E. Schoenfield_, Dec 04 2022