OFFSET
1,1
COMMENTS
Unitary divisors of n are divisors d such that gcd(d,n/d)=1.
Seemingly, a subsequence of A246198 (half-Zumkeller numbers).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Bhabesh Das, On unitary Zumkeller numbers, Notes on Number Theory and Discrete Mathematics, Vol. 30, No. 2 (2024), pp. 436-442.
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
KEYWORD
nonn
AUTHOR
Ivan N. Ianakiev, Aug 03 2017
STATUS
approved