A240968 - OEIS

%I #29 Sep 21 2019 21:56:26

%S 5,8,10,41,206,1066,2412,3281,8086,11570,29525,57012,73728,410390,

%T 413486,775130,2391485,2454146,2937446,64563520,100531166,152032126,

%U 988747406

%N Unitary anti-perfect numbers.

%C For any number x we consider the sum of its anti-divisors which are coprime to x (unitary anti-divisors). The sequence list the numbers for which this sum is equal to x.

%C Subset of A192270.

%C I found only 2 unitary anti-amicable numbers: 18208, 20470.

%C No other terms < 2147000000. _Jud McCranie_, Sep 21 2019.

%e Anti-divisors of 1066 are 3, 4, 9, 27, 52, 79, 164, 237, 711. The anti-divisors which are coprime to 1066 are 3, 9, 27, 79, 237, 711 and their sum is 3 + 9 + 27 + 79 + 237 + 711 = 1066.

%p P:=proc(q) local a,k,n;

%p for n from 3 to q do a:=0; b:=0;

%p for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then

%p   if gcd(n,k)=1 then a:=a+k; fi; fi; od;

%p if n=a then print(n); fi; od; end: P(10^6);

%Y Cf. A066272, A066417, A073930, A192270, A240979.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Aug 05 2014

%E a(14)-a(23) by _Jud McCranie_, Sep 21 2019.