A337738 - OEIS

%I #9 Apr 04 2023 07:43:21

%S 738,3492,14184,58896,236448,954432,2549700,10884600,44989200

%N Terms of A171641 with a record number of divisors.

%C Non-deficient numbers (A023196) with an even sum of divisors (A000203) which cannot be partitioned into two disjoint sets with equal sum, and having a record number of divisors.

%C The corresponding numbers of divisors are 12, 18, 24, 30, 36, 42, 54, 72, 90, ...

%e The number of divisors of each of the first 33 terms of A171641 is 12. A171641(34) = 3492 has 18 divisors, and it is the first term with more than 12 divisors. Therefore, a(2) = 3492.

%t nonZumQ[n_] := Module[{d = Divisors[n], sum, x}, sum = Plus @@ d; sum >= 2*n && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] == 0]; dm = 0; s = {}; Do[d = DivisorSigma[0, n]; If[d > dm, q = nonZumQ[n]; If[q && d > dm, dm = d; AppendTo[s, n]]], {n, 1, 60000}]; s

%Y Cf. A000005, A000203, A023196, A083207, A171641, A335008.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Sep 17 2020

%E a(8)-a(9) from _Amiram Eldar_, Apr 04 2023