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%I #11 Jul 21 2021 00:44:21
%S 1,2,10,84,1155,25740,471240,14549535,535422888
%N Unitary highly composite deficient numbers: unitary deficient numbers k whose number of unitary divisors ud(k) > ud(m) for all unitary deficient numbers m < k.
%C The record numbers of unitary divisors are 1, 2, 4, 8, 16, 32, 64, 128, 256, ...
%C The unitary version of A302934.
%t usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; udiv[n_] := 2^PrimeNu[n]; dm = 0; Do[sig = usigma[n]; If[sig >= 2 n, Continue[]]; d = udiv[n]; If[d > dm, Print[n]; dm = d], {n, 1, 1000000000}]
%o (PARI) nbud(n) = 1<<omega(n);
%o usigma(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));
%o lista(nn) = {my(maxd = 0); for(n=1, nn, if ((usigma(n) < 2*n) && (nbud(n) > maxd), print1(n, ", "); maxd = nbud(n);););} \\ _Michel Marcus_, Apr 17 2018
%Y Cf. A034444, A034448, A129487, A302934.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Apr 16 2018