A357326 Weird untouchable numbers.

836, 7192, 7912, 12670, 13510, 16030, 16310, 16870, 17272, 18830, 21910, 24290, 24430, 26530, 26810, 29470, 31430, 34930, 35210, 35630, 37870, 42910, 43330, 46130, 46270, 48370, 52990, 53830, 57890, 61810, 70910, 73430, 74270, 74410, 76790, 77630, 79030, 82670

Offset: 1

Author

Amiram Eldar, Sep 24 2022

Keywords

• nonn

Comments

Abundant numbers that are not the sum of any subset of their aliquot divisors, and are also not the sum of all the aliquot divisors of any other number.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3776

Crossrefs

Intersection of A005114 and A006037.

Cf. A001065, A005101.

Programs

Mathematica

weirdQ[n_] := Module[{d = Most[Divisors[n]]}, If[Total[d] <= n, False, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0]]; seq[max_] := Module[{s = Table[0, {n, 1, max}], i}, Do[If[(i = DivisorSigma[1, n] - n) <= max, s[[i]]++], {n, 2, (max - 1)^2}]; Select[Position[s, 0] // Flatten, weirdQ]]; seq[8000]