A323342 Numbers k whose bi-unitary divisors have an even sum which is larger than 2k, but they cannot be partitioned into two disjoint parts whose sums are equal.

704, 1458, 2394, 7544, 10184, 46400, 60416, 106434, 115182, 118098, 121014, 125000, 129762, 141426, 147258, 150174, 156006, 158922, 164754, 176418, 185166, 190998, 199746, 202662, 217242, 220158, 228906, 237654, 243486, 246402, 252234, 260982, 263898, 278478

Offset

1,1

Comments

The bi-unitary version of A171641.

Links

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

Mathematica

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[n_] := Select[Divisors[n], Last@Intersection[f@#, f[n/#]] == 1 &]; fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[n_] := If[n==1, 1, Times @@ (fun @@@ FactorInteger[n])]; seq={}; Do[s=bsigma[n]; If[OddQ[s] || s<=2n, Continue[]]; div = bdiv[n]; If[Coefficient[Times @@ (1 + x^div) // Expand, x, s/2] == 0, AppendTo[seq, n]], {n, 1, 10000}]; seq

Crossrefs

Cf. A171641, A188999, A292982, A323341, A323343, A323344.

Sequence in context: A186923 A185807 A105846 * A237009 A185568 A185799

Adjacent sequences: A323339 A323340 A323341 * A323343 A323344 A323345

Keyword

nonn

Author

Amiram Eldar, Jan 11 2019

Status

approved