A370355 Highly touchable numbers sandwiched between untouchable twin pairs.

1681, 5251, 7771, 36961, 39271, 170941, 196351, 360361, 510511, 1009471, 9699691

Offset: 1

Author

Amiram Eldar, Feb 16 2024

Keywords

• nonn
• hard
• more

Comments

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.

Crossrefs

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

Cf. A001065, A005114.

Similar sequences: A068507, A113839.

Programs

Mathematica

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]