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

Author

Amiram Eldar, Nov 07 2019

Keywords

• nonn

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)

Crossrefs

Intersection of A006037 and A111592.

Cf. A005835, A258250.

Programs

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[#] &]