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A335202
Unitary Zumkeller numbers (A290466) whose set of unitary divisors can be partitioned into two disjoint sets of equal sum in a single way.
4
6, 60, 70, 90, 3230, 3770, 4030, 4510, 5170, 5390, 5830, 50388, 87360, 269990, 442365, 544310, 592670, 740870, 1341230, 1772870, 4173070, 4199030, 5719266, 5728842, 5743206, 34473582, 624032630, 812851182, 1109686930, 1113445430, 2280959890, 55157757606
OFFSET
1,1
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..48 (terms < 10^12)
EXAMPLE
60 is a term since there is only one partition of its set of unitary divisors, {1, 3, 4, 5, 12, 15, 20, 60}, into 2 disjoint sets whose sum is equal: 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60.
MATHEMATICA
uzQ[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] == 2]]; Select[Range[6000], uzQ]
CROSSREFS
The unitary version of A083209.
Subsequence of A290466.
A002827 is a subsequence.
Sequence in context: A308413 A204093 A136927 * A061475 A295830 A335937
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 26 2020
EXTENSIONS
Terms a(19) and beyond from Giovanni Resta, May 30 2020
STATUS
approved