A331974 Infinitary highly touchable numbers: numbers m > 1 such that a record number of numbers k have m as the sum of the proper infinitary divisors of k.

2, 6, 8, 17, 21, 37, 49, 55, 67, 79, 85, 91, 121, 151, 175, 181, 211, 295, 301, 361, 391, 421, 481, 511, 571, 631, 781, 841, 991, 1051, 1231, 1261, 1471, 1561, 1651, 1681, 1891, 2101, 2311, 2731, 3151, 3361, 3571, 3991, 4201, 4291, 4411, 4621, 5251, 5461, 6091

Offset: 1

Author

Amiram Eldar, Feb 03 2020

Keywords

• nonn

Comments

The corresponding record values are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...

The infinitary version of A238895.

Examples

			a(1) = 2 since it is the first number which is not the sum of proper infinitary divisors of any number.
a(2) = 6 since it is the least number which is the sum of proper infinitary divisors of one number: 6 = A126168(6).
a(3) = 8 since it is the least number which is the sum of proper infinitary divisors of 2 numbers: 8 = A126168(10) = A126168(12).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..76 (terms below 30000)

Crossrefs

Cf. A049417, A077609, A126168, A238895, A324277, A325177, A331972, A331973.

Programs

Mathematica

fun[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ (fun @@@ FactorInteger[n]); is[n_] := isigma[n] - n; m = 300; v = Table[0, {m}]; Do[i = is[k]; If[2 <= i <= m, v[[i]]++], {k, 1, m^2}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 2, m}]; s