A240979 Sum of unitary anti-divisors of n.

0, 0, 2, 3, 5, 0, 10, 8, 2, 10, 12, 5, 19, 12, 2, 14, 28, 12, 18, 16, 2, 32, 34, 7, 29, 20, 18, 38, 24, 0, 42, 58, 20, 26, 28, 0, 50, 66, 20, 39, 41, 22, 56, 32, 22, 54, 60, 24, 58, 56, 2, 86, 88, 0, 42, 40, 30, 92, 90, 35, 57, 74, 32, 46, 48, 26, 132, 104, 2

Offset: 1

Author

Paolo P. Lava, Aug 06 2014

Keywords

• nonn

Comments

For unitary anti-divisors of n are intended all the anti-divisors of n which are coprime to n.

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066272, A066417, A242029.

Programs

Maple

P:=proc(q) local a,k,n,v; v:=[]; for n from 1 to q do a:=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; v:=[op(v),a]; od; print(op(v)); end: P(69);
# corrected by Paolo P. Lava, Aug 17 2024

Mathematica

antiDivisors[n_Integer] := Cases[Range[2, n - 1], ?(Abs[Mod[n, #] - #/2] < 1 &)]; a240979[n_Integer] := Total[Select[antiDivisors[n], CoprimeQ[#, n] &]]; a240979 /@ Range[120] (* _Michael De Vlieger, Aug 17 2014 *)

Formula

Anti-divisors of 14 are 3, 4, 9. Anti-divisors coprime to 14 are 3 and 9 and therefore a(14) = 3 + 9 = 12.