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%I #4 Mar 06 2020 22:40:19
%S 1,2,8,14,44,104,224,495,735,2024,2079,5264,5984,21735,126224,201824,
%T 862784,1890944,2821455,6116175,7316000,14753024,23014719,38127375,
%U 80061344,205466624,391738599,879207615,1794220064,3199900599,3809727999,16916370624
%N Numbers m such that min(d(m), d(m+1)) > min(d(k), d(k+1)) for all k < m, where d(m) is the number of divisors of m (A000005).
%C The corresponding values of min(d(a(n)), d(a(n)+1)) are 1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 20, 24, 32, 40, 48, 56, 64, 72, 80, 96, 108, 112, 120, 144, 160, 192, 224, 240, 256, 288, 320, ...
%e The values of min(d(k), d(k+1)) for k = 1, 2, ... 8 are 1, 2, 2, 2, 2, 2, 2, 3. The record values in this range, 1, 2 and 3, are obtained at k = 1, 2, and 8.
%t seq={}; dminmax = 0; d1 = 1; Do[d2 = DivisorSigma[0, n];dmin = Min[d1, d2]; If[dmin > dminmax, dminmax = dmin; AppendTo[seq, n-1]]; d1 = d2, {n, 2, 10^6}]; seq
%Y Cf. A000005, A002182, A123000, A175143, A333054.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Mar 06 2020
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