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A294528 a(n) is the smallest prime that begins a run of exactly n consecutive numbers having 2, 4, ..., 2*n divisors.

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%I A294528 #23 Feb 07 2021 14:55:26
%S A294528 2,5,61,421,1524085621
%N A294528 a(n) is the smallest prime that begins a run of exactly n consecutive numbers having 2, 4, ..., 2*n divisors.
%C A294528 No such run exists for any n > 5; for a proof, see Links.
%H A294528 Jon E. Schoenfield, <a href="/A294528/a294528_1.txt">A proof that a(5) is the final term of this sequence</a>
%e A294528 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 A294528 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 A294528 Cf. A075028, A284596, A341213.
%K A294528 nonn,fini,full
%O A294528 1,1
%A A294528 _Jon E. Schoenfield_, Nov 01 2017