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%I #9 Feb 07 2019 23:48:50
%S 1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,31,32,33,34,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50,51,
%U 52,53,54,55,56,57,58,59,61,62,63,64,65,67,68,69,71,72,73,74,75,76,77,79
%N Unitary deficient numbers.
%C The unitary deficient numbers account for almost 93% of all integers (including all primes (A000040) and prime powers (A000961)) and asymptotically satisfy a(n)~1.0753n. This provides an excellent fit as n grows larger. For example, the one millionth unitary deficient number is 1075293 and the asserted approximation returns 1075300, giving an error of only 0.00065%.
%H Nathaniel Johnston, <a href="/A129487/b129487.txt">Table of n, a(n) for n = 1..10000</a>
%F Integers for which A034460(n) < n, or equivalently for which A034448(n) < 2n.
%e The sixth integer that exceeds the sum of its proper unitary divisors is 7. Hence a(6)=7.
%p a := proc(n) numtheory[divisors](n); select(d -> igcd(d,n/d)=1,%); `if`(add(i,i=%) < 2*n,n,NULL) end: # _Peter Luschny_, May 03 2009
%t UnitaryDivisors[n_Integer?Positive]:=Select[Divisors[n],GCD[ #,n/# ]==1&];Select[Range[100],Plus@@UnitaryDivisors[ # ]-2#<0 &]
%Y Cf. A034460, A034448, A129468, A034683, A000040, A000961.
%K easy,nonn
%O 1,2
%A _Ant King_, Apr 20 2007
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