%I #8 Nov 21 2021 05:06:52

%S 4,10,1,19940,54584,204323,2789143044,27092041443

%N a(n) is the start of the least run of exactly n consecutive numbers with the same number of nonunitary divisors.

%C a(9) > 10^11, if it exists.

%e a(2) = 10 since A048105(10) = A048105(11) = 0, and A048105(9) != 0 and A048105(12) != 0.

%t d[n_] := DivisorSigma[0, n] - 2^PrimeNu[n]; seq[len_, nmax_] := Module[{s = Table[0, {len}], dprev = -1, n = 1, c = 0, k = 0}, While[k < len && n < nmax, d1 = d[n]; If[d1 == dprev, c++, If[c > 0 && c <= len && s[[c]] == 0, k++; s[[c]] = n - c]; c = 1]; n++; dprev = d1]; TakeWhile[s, # > 0 &]]; seq[6, 10^6]

%Y Cf. A048105, A344315.

%Y Similar sequences: A006558, A045983, A048932, A067813, A077657, A318166.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Nov 14 2021