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

Author

Amiram Eldar, Sep 17 2020

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Intersection of A006037 and A171641.

Cf. A000203, A083207.

Programs

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]