A294906 a(n) is the least squarefree integer, product of n primes that are symmetrically distributed around their average.

2, 6, 105, 2145, 53295, 1616615, 57998985, 3038795305, 3907126810041, 7292509103495, 66240019730740785, 82246340873964085, 1870667082297874652055, 343515424581301546805, 9160656702012692171113335, 2356596317899272514936585, 1903895854998638367242867256645

Offset: 1

Author

Michel Marcus, Nov 10 2017

Keywords

• nonn

Examples

			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], ...
		

Crossrefs

Cf. A262723, A294751, A294752, A294776.

Programs

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););}
a(n) = {my(k = prod(i=1, n, prime(i))); while (! isok(k, n), k++); k;}

Extensions

a(8)-a(17) from Giovanni Resta, Nov 10 2017