A337740 Weird numbers (A006037) with an even sum of divisors that are not Zumkeller numbers (A083207).

73616, 682592, 2081824, 3963968, 4960448, 5440192, 6621632, 8000704, 8134208, 12979264, 31297472, 33736064, 43955584, 55691392, 58433152, 58904704, 160074368, 254533504, 263654656, 266828032, 267369728, 272240768, 352668416, 353383168, 357542656, 431462656, 530110208

Offset

1,1

Comments

Non-deficient numbers (A023196) with an even sum of divisors (A000203) that are neither pseudoperfect numbers (A005835) nor Zumkeller numbers (A083207).

Equivalently, numbers k such that sigma(k) >= 2*k and sigma(k) == 0 (mod 2), such that no subset of the aliquot divisors of k sums to k or to sigma(k)/2.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

73616 is a term since sigma(73616) = 147312 is even and larger than 2 * 73616 = 147232. No subset of the aliquot divisors of 73616 sums to 73616 or to sigma(73616)/2 = 73656.

Mathematica

seqQ[n_] := Module[{d = Divisors[n], sum, c, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, c = CoefficientList[Product[1 + x^i, {i, d}], x]; c[[1 + 2*n]] == 0 && c[[1 + sum/2]] == 0]]; Select[Range[10^6], seqQ]

Crossrefs

Intersection of A006037 and A171641.

Cf. A000203, A083207.

Sequence in context: A250838 A365309 A105648 * A180300 A172640 A172741

Adjacent sequences: A337737 A337738 A337739 * A337741 A337742 A337743

Keyword

nonn

Author

Amiram Eldar, Sep 17 2020

Status

approved