A240979 -id:A240979 - cp's OEIS frontend

A242029 Number of anti-divisors m <= n of n that are coprime to n.

0, 0, 1, 1, 2, 0, 3, 2, 1, 2, 3, 1, 4, 2, 1, 2, 5, 2, 3, 2, 1, 4, 5, 1, 4, 2, 3, 4, 3, 0, 5, 6, 3, 2, 3, 0, 5, 6, 3, 3, 4, 2, 5, 2, 3, 4, 5, 2, 5, 4, 1, 6, 7, 0, 3, 2, 3, 6, 7, 3, 4, 4, 3, 2, 3, 2, 9, 6, 1, 2, 5, 4, 7, 4, 1, 4, 7, 2, 3, 4, 3, 6, 7, 1, 6, 4, 5

Offset: 1

Michael De Vlieger, Aug 11 2014

nonn

See A066272 for the definition of anti-divisor; that sequence gives the number of anti-divisors m < n of n.

All the anti-divisors m < n of prime n must be coprime to n, since any integer k > 1 must either divide or be coprime to prime n, and since no anti-divisor m can divide n.

			a(3) = 1 and A066272(3) = 1 because the set of anti-divisors of 3 = {2} and 2 is coprime to 3.
a(6) = 0 and A066272(6) = 1 because the set of anti-divisors of 6 = {4} but 4 is not coprime to 6.
a(12) = 1 and A066272(12) = 2 because the set of anti-divisors of 12 = {5, 8}, but only 5 is coprime to 12.

Michael De Vlieger, Table of n, a(n) for n = 1..10000
M. De Vlieger, Arithmetic Relationships between Antidivisors k < n and n

Cf. A066272, A240979.

antiDivisors[n_Integer] := Cases[Range[2, n - 1], ?(Abs[Mod[n, #] - #/2] < 1 &)]; a242029[n_Integer] := Length[Select[antiDivisors[n], CoprimeQ[#, n] &]]; Table[a242029[k], {k, 100}] (* _Michael De Vlieger, Aug 11 2014 *)

A240968 Unitary anti-perfect numbers.

Original entry on oeis.org

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

Paolo P. Lava, Aug 05 2014

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.

			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.

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

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);

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

cp's OEIS Frontend

A242029 Number of anti-divisors m <= n of n that are coprime to n.

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