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A121940 Product of the first n primes of the form 6k+1.

%I A121940 #36 Oct 23 2022 23:38:55
%S A121940 7,91,1729,53599,1983163,85276009,5201836549,348523048783,
%T A121940 25442182561159,2009932422331561,194963444966161417,
%U A121940 20081234831514625951,2188854596635094228659,277984533772656967039693,38639850194399318418517327,5834617379354297081196116377
%N A121940 Product of the first n primes of the form 6k+1.
%C A121940 For n>1, a(n) is the least positive integer that can be primitively represented as m^2+mn+n^2 with 0<=m<=n and gcd(m,n)=1 in exactly 2^(n-1) ways. - _Ray Chandler_, Oct 01 2007
%C A121940 From _Bernard Schott_, Mar 30 2021: (Start)
%C A121940 Also, for n >= 1, a(n) is the smallest positive integer m such that m^2 can be primitively represented as k^2-k*q+q^2 with 1 <= k < q and gcd(k,q)= 1 in exactly 2^n ways. For example (a(1))^2 = 7^2 = 3^2 - 3*8 + 8^2 = 5^2 - 5*8 + 8^2.
%C A121940 It follows that a(n) is the smallest middle side b that appears exactly 2^n times consecutively in the data of A335895, for integer-sided triangles whose angles A < B < C are in arithmetic progression. (End)
%C A121940 Also, a(n) is the smallest largest side c that appears exactly 2^(n-1) times consecutively in the data of A357277 for integer-sided triangles with angles A < B < C = 2*Pi/3 = 120 degrees. - _Bernard Schott_, Oct 21 2022
%H A121940 Ray Chandler, <a href="/A121940/b121940.txt">Table of n, a(n) for n=1..100</a>
%F A121940 a(n) = Product_{i=1..n} A002476(i).
%e A121940 a(4) = 53599 = 7 * 13 * 19 * 31.
%t A121940 Rest@FoldList[Times, 1, Select[6 Range[100] + 1, PrimeQ]] (* _Ray Chandler_, Oct 01 2007 *)
%o A121940 (PARI) lista(nn) = {my(pr=1, list=List()); forprime(p=1, nn, if ((p%3) == 1, listput(list,pr *= p));); Vec(list);} \\ _Michel Marcus_, Jul 17 2020
%Y A121940 Cf. A002476, A002110, A006278, A078586, A335895.
%Y A121940 Greedy inverse of A005088.
%K A121940 easy,nonn
%O A121940 1,1
%A A121940 _Jonathan Vos Post_, Sep 03 2006
%E A121940 Extended by _Ray Chandler_, Oct 01 2007