

A290467


Unitary halfZumkeller numbers: numbers k whose unitary proper divisors can be partitioned into two disjoint sets whose sums are equal.


2



6, 12, 20, 30, 42, 56, 60, 66, 70, 72, 78, 84, 90, 102, 114, 120, 138, 150, 168, 174, 180, 186, 210, 220, 222, 240, 246, 252, 258, 272, 280, 282, 294, 318, 330, 354, 360, 364, 366, 390, 402, 420, 426, 438, 440, 462, 474, 498, 510, 520, 532, 534, 546, 560, 570, 582, 606, 618
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OFFSET

1,1


COMMENTS

Unitary divisors of n are divisors d such that gcd(d,n/d)=1.
Seemingly, a subsequence of A246198 (halfZumkeller numbers).


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Unitary Divisor Function
Wikipedia, Unitary divisor


EXAMPLE

The set of unitary proper divisors of 12 is {1,3,4}. It can be partitioned into two disjoint subsets with equal sums of elements: {1,3} and {4}, therefore 12 is in the sequence.


MATHEMATICA

uPropDiv[n_/; n>1]:=Block[{d=Most[Divisors[n]]}, Select[d, GCD[#, n/#]==1&]]; uhZNQ[n_]:=Module[{d=uPropDiv[n], t, ds, x}, ds=Plus@@d; If[Mod[ds, 2]>0, False, t=CoefficientList[Product[1+x^i, {i, d}], x]; t[[1+ds/2]]>0]]; Select[Range[10^3], uhZNQ] (* combined from the code by Robert G. Wilson v at A034448 and T. D. Noe at A083207 *)


CROSSREFS

Cf. A083207, A246198, A290466.
Sequence in context: A083209 A080714 A116368 * A007622 A180291 A056930
Adjacent sequences: A290464 A290465 A290466 * A290468 A290469 A290470


KEYWORD

nonn


AUTHOR

Ivan N. Ianakiev, Aug 03 2017


STATUS

approved



