A370355 - OEIS

%I #6 Feb 16 2024 15:21:16

%S 1681,5251,7771,36961,39271,170941,196351,360361,510511,1009471,

%T 9699691

%N Highly touchable numbers sandwiched between untouchable twin pairs.

%C Highly touchable numbers k have a record number of solutions x to A001065(x) = k, while untouchable numbers k have no solution to this equation.

%t seq[nmax_] := Module[{v = Table[0, {nmax}], i, s = {}, vmax = -1}, Do[i = DivisorSigma[1, n] - n; If[0 < i <= nmax, v[[i]]++], {n, 1, nmax^2}]; Do[If[v[[n]] > vmax, vmax = v[[n]]; If[v[[n - 1]] == 0 && v[[n + 1]] == 0, AppendTo[s, n]]], {n, 2, nmax - 1}]; s]; seq[8000]

%Y Intersection of A238895 and {A231964(n) + 1};

%Y Cf. A001065, A005114.

%Y Similar sequences: A068507, A113839.

%K nonn,hard,more

%O 1,1

%A _Amiram Eldar_, Feb 16 2024