The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A335220 Exponential Zumkeller numbers (A335218) whose set of exponential divisors can be partitioned into two disjoint sets of equal sum in a record number of ways. 0
 36, 900, 3600, 22500, 44100, 176400, 705600, 1587600, 4410000, 5336100, 21344400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding record values are 1, 3, 4, 6, 83, 2920, 81080, 254566, 344022, 487267, 4580715031, ... LINKS EXAMPLE 36 is the first term since it is the least exponential Zumkeller number, and its exponential divisors, {6, 12, 18, 36}, can be partitioned in a single way: 6 + 12 + 18 = 36. The next exponential Zumkeller number with more than one partition is 900, whose nonunitary divisors, {30, 60, 90, 150, 180, 300, 450, 900}, can be partitioned in 3 ways: 30 + 60 + 90 + 150 + 300 + 450 = 180 + 900, 60 + 90 + 180 + 300 + 450 = 30 + 150 + 900, and 150 + 180 + 300 + 450 = 30 + 60 + 90 + 900. 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]]]}]]; eDivs[n_] := Module[{d = Rest[Divisors[n]]}, Select[d, expDivQ[n, #] &]]; nways[n_] := Module[{d = eDivs[n], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], 0, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]]/2]]; nwaysm = 0; s = {}; Do[nways1 = nways[n]; If[nways1 > nwaysm, nwaysm = nways1; AppendTo[s, n]], {n, 1, 23000}]; s CROSSREFS The exponential version of A083212. Subsequence of A335218. Cf. A335219. Sequence in context: A001812 A229680 A169836 * A248108 A233003 A075916 Adjacent sequences:  A335217 A335218 A335219 * A335221 A335222 A335223 KEYWORD nonn,more AUTHOR Amiram Eldar, May 27 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)