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%I #12 Feb 25 2024 06:00:05
%S 2,6,105,2145,53295,1616615,57998985,3038795305,3907126810041,
%T 7292509103495,66240019730740785,82246340873964085,
%U 1870667082297874652055,343515424581301546805,9160656702012692171113335,2356596317899272514936585,1903895854998638367242867256645
%N a(n) is the least squarefree integer, product of n primes that are symmetrically distributed around their average.
%e The prime factors of the first terms are: [2], [2, 3], [3, 5, 7], [3, 5, 11, 13], [3, 5, 11, 17, 19], [5, 7, 11, 13, 17, 19], [3, 5, 11, 17, 23, 29, 31], ...
%o (PARI) isok(n, nb) = {if (issquarefree(n) && (omega(n)==nb), f = factor(n)[, 1]~; avg = vecsum(f)/#f; for (k=1, #f\2, if (f[k] + f[#f-k+1] != 2*avg, return(0));); return (1););}
%o a(n) = {my(k = prod(i=1, n, prime(i))); while (! isok(k, n), k++); k;}
%Y Cf. A262723, A294751, A294752, A294776.
%K nonn
%O 1,1
%A _Michel Marcus_, Nov 10 2017
%E a(8)-a(17) from _Giovanni Resta_, Nov 10 2017
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