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A373560 a(n) is the smallest multiple of prime(n)^2 that starts a run of 5 consecutive integers with 6 divisors, or -1 if no such multiple exists.

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%I A373560 #9 Jun 10 2024 14:56:53
%S A373560 -1,-1,-1,10093613546512321,-1,-1,7700031346933907521,-1,
%T A373560 5344962129269790721,-1,20453982425165652721,-1,8163195338222675521,
%U A373560 -1,2467958104789157112721,-1,-1,-1,-1,14666767069023896053921,212170739123852995921,287954235303137500060321,-1,84769922583214545304321
%N A373560 a(n) is the smallest multiple of prime(n)^2 that starts a run of 5 consecutive integers with 6 divisors, or -1 if no such multiple exists.
%C A373560 Terms were obtained using the b-file at A141621.
%C A373560 a(n) = -1 if prime(n) is not in A001132.
%C A373560 Conjecture: the converse is also true.
%e A373560 a(1) = a(2) = a(3) = -1 because the first of five consecutive integers having six divisors is never a multiple of 2^2, 3^2, or 5^2.
%e A373560 a(4) = 10093613546512321 because it is the smallest term in A141621 that is a multiple of prime(4)^2 = 49.
%e A373560 a(9) = 5344962129269790721 because it is the smallest term in A141621 that is a multiple of prime(9)^2 = 23^2.
%Y A373560 Cf. A001132, A030515, A042999, A054753, A141621.
%K A373560 sign
%O A373560 1,4
%A A373560 _Jon E. Schoenfield_, Jun 09 2024