A349305 a(n) is the start of the least run of exactly n consecutive numbers with the same number of nonunitary divisors.

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

Offset: 1

Author

Amiram Eldar, Nov 14 2021

Keywords

• nonn
• more

Comments

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

Examples

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

Crossrefs

Cf. A048105, A344315.

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

Programs

Mathematica

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]