A337738 Terms of A171641 with a record number of divisors.

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

Offset

1,1

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, ...

Links

Table of n, a(n) for n=1..9.

Example

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.

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

Crossrefs

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

Sequence in context: A251814 A320714 A251647 * A204289 A204285 A224564

Adjacent sequences: A337735 A337736 A337737 * A337739 A337740 A337741

Keyword

nonn,more

Author

Amiram Eldar, Sep 17 2020

Extensions

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

Status

approved