A240968 Unitary anti-perfect numbers.

5, 8, 10, 41, 206, 1066, 2412, 3281, 8086, 11570, 29525, 57012, 73728, 410390, 413486, 775130, 2391485, 2454146, 2937446, 64563520, 100531166, 152032126, 988747406

Offset: 1

Author

Paolo P. Lava, Aug 05 2014

Keywords

• nonn
• more

Comments

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.

Subset of A192270.

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

No other terms < 2147000000. Jud McCranie, Sep 21 2019.

Examples

			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.
		

Crossrefs

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

Programs

Maple

P:=proc(q) local a,k,n;
for n from 3 to q do a:=0; b:=0;
for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then
  if gcd(n,k)=1 then a:=a+k; fi; fi; od;
if n=a then print(n); fi; od; end: P(10^6);

Extensions

a(14)-a(23) by Jud McCranie, Sep 21 2019.