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

1,3

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

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.

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 *)

Crossrefs

Cf. A066272, A066417, A242029.

Sequence in context: A096535 A126047 A023049 * A368819 A171034 A062007

Adjacent sequences: A240976 A240977 A240978 * A240980 A240981 A240982

Keyword

nonn

Author

Paolo P. Lava, Aug 06 2014

Status

approved