A329190 Weird admirable numbers: numbers that are both weird (A006037) and admirable (A111592).

70, 836, 4030, 5830, 7192, 7912, 10792, 17272, 45356, 83312, 91388, 113072, 243892, 254012, 388076, 786208, 1713592, 4145216, 4199030, 4632896, 9928792, 11547352, 13086016, 15126992, 17999992, 29465852, 29581424, 34869056, 74899952, 89283592, 95327216, 120888092

Offset

1,1

Comments

Admirable numbers that are not pseudoperfect (A005835).

Differs from A258250 at n >= 13.

Links

Amiram Eldar, Table of n, a(n) for n = 1..66 (terms below 10^11)

Mathematica

admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2]; 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]]; Select[Range[10000], admQ[#] && weirdQ[#] &]

Crossrefs

Intersection of A006037 and A111592.

Cf. A005835, A258250.

Sequence in context: A006037 A002975 A354282 * A258250 A349285 A335008

Adjacent sequences: A329187 A329188 A329189 * A329191 A329192 A329193

Keyword

nonn

Author

Amiram Eldar, Nov 07 2019

Status

approved