A323343 Numbers k whose exponential divisors have an even sum which is larger than 2k, but they cannot be partitioned into two disjoint parts whose sums are equal.

1910412, 9552060, 21014532, 24835356, 32477004, 43939476, 55401948, 59222772, 70685244, 78326892, 82147716, 89789364, 101251836, 105072660, 112714308, 116535132, 124176780, 127997604, 135639252, 139460076, 150922548, 158564196, 162385020, 170026668, 185309964

Offset: 1

Author

Amiram Eldar, Jan 11 2019

Keywords

• nonn

Comments

The exponential version of A171641.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A051377, A129575, A171641, A323341, A323342, A323344.

Programs

Mathematica

dQ[n_, m_] := (n>0&&m>0 &&Divisible[n, m]); expDivQ[n_, d_] := Module[ {ft = FactorInteger[n]}, And@@MapThread[dQ, {ft[[;; , 2]], IntegerExponent[ d, ft[[;; , 1]]]} ]]; ediv[n_] := Module[ {d=Rest[Divisors[n]]}, Select[ d, expDivQ[n, #]&]]; esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[ Last[#]]}] &) /@ FactorInteger[n]; seq={}; Do[s=esigma[n]; If[OddQ[s] || s<=2n, Continue[]]; div = ediv[n]; If[Coefficient[Times @@ (1 + x^div) // Expand, x, s/2] == 0, AppendTo[seq, n]], {n, 1, 10000}]; seq