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%I #19 Apr 29 2019 02:43:35
%S 2,1,73,61,35521,11371,7392171,168776043,1584614377,38045133481
%N a(n) is the minimum number that is the first of n consecutive integers with an increasing number of divisors.
%C Comment from _Giovanni Resta_, Apr 02 2017: (Start)
%C In A075028 the chain has to be at least of length k, whereas here it has to be of length exactly k.
%C Here a(2) = 1, because d(1)=1, d(2)=2, d(3)=2, so the first chain of 2 starts at 1.
%C (End)
%C Calculated with a brute force C++ program.
%C a(11) > 10^13. - _Giovanni Resta_, Apr 14 2017
%e 61 => 61^1 => 2 divisors
%e 62 => 2^1 * 31^1 => 4 divisors
%e 63 => 3^2 * 7 => 6 divisors
%e 64 => 2^6 => 7 divisors
%e 65 => 5^1 * 13^1 => 4 divisors.
%e So 61 is the first of four consecutive numbers with an increasing number of divisors. 65 breaks that chain. 61 is the minimum such number so it is the 4th number in the sequence.
%Y See A075028 for another version.
%K hard,more,nonn
%O 1,1
%A _Fred Schneider_, Mar 29 2017
%E Name clarified by _Jon E. Schoenfield_, Apr 28 2019