A337738 Terms of A171641 with a record number of divisors.

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

Offset: 1

Author

Amiram Eldar, Sep 17 2020

Keywords

• nonn
• more

Comments

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.

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

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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

Extensions

a(8)-a(9) from Amiram Eldar, Apr 04 2023