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

1,1

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.

Links

Table of n, a(n) for n=1..23.

Example

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.

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);

Crossrefs

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

Sequence in context: A185001 A057154 A072524 * A187878 A191233 A314386

Adjacent sequences: A240965 A240966 A240967 * A240969 A240970 A240971

Keyword

nonn,more

Author

Paolo P. Lava, Aug 05 2014

Extensions

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

Status

approved