A337739 Terms of A083209 with a record number of divisors.

6, 12, 56, 176, 550, 2752, 3230, 8925, 351351

Offset

1,1

Comments

Zumkeller numbers (A083207) which can be partitioned into two disjoint sets with an equal sum in a single way, and having a record number of divisors.

The corresponding numbers of divisors are 4, 6, 8, 10, 12, 14, 16, 24, 48, ...

a(10) > 1.8*10^6.

Per a comment by T. D. Noe in A083209 we have a(10) <= 2^24 * 11184829 = 187650292056064 and this sequence is infinite. - David A. Corneth, May 19 2021

Links

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

Example

The first 5 terms of A083209 are 6, 12, 20, 28, 56. Their numbers of divisors are 4, 6, 6, 6, 8. The record values, 4, 6 and 8 occur at 6, 12 and 56.

Mathematica

zumsingleQ[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]] == 2]; dm = 0; s = {}; Do[d = DivisorSigma[0, n]; If[d > dm, q = zumsingleQ[n]; If[q && d > dm, dm = d; AppendTo[s, n]]], {n, 1, 10^4}]; s

Crossrefs

Cf. A000005, A000203, A023196, A083207, A083209, A335008, A337738.

Sequence in context: A324529 A076722 A322288 * A076305 A088944 A335000

Adjacent sequences: A337736 A337737 A337738 * A337740 A337741 A337742

Keyword

nonn,more

Author

Amiram Eldar, Sep 17 2020

Status

approved