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A337740 Weird numbers (A006037) with an even sum of divisors that are not Zumkeller numbers (A083207). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A242805 A250838 A105648 * A180300 A172640 A172741

Adjacent sequences:  A337737 A337738 A337739 * A337741 A337742 A337743

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 17 2020

STATUS

approved

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Last modified August 12 08:38 EDT 2022. Contains 356067 sequences. (Running on oeis4.)