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

1,1

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

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]

Crossrefs

Intersection of A005114 and A006037.

Cf. A001065, A005101.

Sequence in context: A235288 A162945 A138850 * A322524 A016113 A177846

Adjacent sequences: A357323 A357324 A357325 * A357327 A357328 A357329

Keyword

nonn

Author

Amiram Eldar, Sep 24 2022

Status

approved