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A348420 a(n) = Product_{k=1..n} (p_k - 1)/2 where p_1, p_2, ..., p_n are the first n primes congruent to 3 modulo 4.

%I A348420 #14 Oct 20 2021 07:12:51
%S A348420 1,1,3,15,135,1485,22275,467775,10758825,312005925,10296195525,
%T A348420 360366843375,14054306891625,576226582556625,29387555710387875,
%U A348420 1557540452650557375,98125048516985114625,6378128153604032450625,440090842598678239093125
%N A348420 a(n) = Product_{k=1..n} (p_k - 1)/2 where p_1, p_2, ..., p_n are the first n primes congruent to 3 modulo 4.
%C A348420 a(n) is the number of coprime squares modulo A348418(n+2), where A348418(n) is the smallest k with rank((Z/kZ)*) = n such that there are an odd number of coprime squares modulo k. (The rank of a finitely generated group rank(G) is defined to be the size of the minimal generating sets of G. In particular, rank((Z/kZ)*) = 0 if k <= 2 and A046072(k) otherwise.)
%H A348420 Jianing Song, <a href="/A348420/b348420.txt">Table of n, a(n) for n = 0..200</a>
%F A348420 a(n) = Product_{k=1..n} (A002145(k) - 1)/2.
%F A348420 a(n) = A046073(A348418(n+2)).
%e A348420 A348418(2) = 8, and the number of coprime squares modulo 8 is a(0) = 1;
%e A348420 A348418(3) = 8 * 3 = 24, and the number of coprime squares modulo 24 is a(1) = (3-1)/2 = 1;
%e A348420 A348418(4) = 8 * 3 * 7 = 168, and the number of coprime squares modulo 168 is a(2) = ((3-1)/2) * ((7-1)/2) = 3;
%e A348420 A348418(5) = 8 * 3 * 7 * 11 = 1848, and the number of coprime squares modulo 1848 is a(3) = ((3-1)/2) * ((7-1)/2) * ((11-1)/2) = 15;
%e A348420 A348418(6) = 8 * 3 * 7 * 11 * 19 = 35112, and the number of coprime squares modulo 35112 is a(4) = ((3-1)/2) * ((7-1)/2) * ((11-1)/2) * ((19-1)/2) = 135.
%o A348420 (PARI) a(n) = my(t=1); forprime(p=2, , if(p%4==3, t*=(p-1)/2; if(n--<1, return(t)))) \\ following _Charles R Greathouse IV_'s program for A078586
%Y A348420 Cf. A002145, A046073, A348418, A046072, A323739.
%K A348420 nonn,easy
%O A348420 0,3
%A A348420 _Jianing Song_, Oct 18 2021