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

1,1

Comments

The exponential version of A171641.

Links

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

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

Crossrefs

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

Sequence in context: A182360 A133542 A215568 * A186802 A179226 A166002

Adjacent sequences: A323340 A323341 A323342 * A323344 A323345 A323346

Keyword

nonn

Author

Amiram Eldar, Jan 11 2019

Status

approved