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%I #23 Feb 07 2021 14:55:26
%S 2,5,61,421,1524085621
%N a(n) is the smallest prime that begins a run of exactly n consecutive numbers having 2, 4, ..., 2*n divisors.
%C No such run exists for any n > 5; for a proof, see Links.
%H Jon E. Schoenfield, <a href="/A294528/a294528_1.txt">A proof that a(5) is the final term of this sequence</a>
%e a(3) = 61 because 61 (prime), 62 = 2*31, and 63 = 3^2*7 have 2, 4, and 6 divisors, respectively (and 64 does not have exactly 8 divisors, so 63 is the last number in the run), and there is no smaller number having this property.
%e a(5) = 1524085621 because the 5 consecutive integers 1524085621..1524085625 have 2, 4, 6, 8, and 10 divisors, respectively (and 1524085626 does not have exactly 12 divisors), and there is no smaller number having this property.
%Y Cf. A075028, A284596, A341213.
%K nonn,fini,full
%O 1,1
%A _Jon E. Schoenfield_, Nov 01 2017
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