OFFSET
1,3
COMMENTS
Alternating row sums of A056538. - Omar E. Pol, Feb 17 2024
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
Equals A054525 * A134871; i.e., Mobius transform of [1, 2, 3, 5, 5, 8, 7, 10, 10, 12, 11, ...]. - Gary W. Adamson, Nov 14 2007
a(n) = Sum_{i=1..n} (A135539(n,i) mod 2). - Ridouane Oudra, Nov 23 2022
EXAMPLE
Divisors of 20: {1,2,4,5,10,20} therefore a(20) = 20 - 10 + 5 - 4 + 2 - 1 = 12.
MAPLE
with(numtheory): a:=proc(n) local k, t:=0, A:=divisors(n); for k to tau(n) do t:= t+A[k]*(-1)^(tau(n)-k) end do; return t; end proc; seq(a(n), n=1..60); # Ridouane Oudra, Nov 23 2022
MATHEMATICA
a[n_] := Plus @@ (-(d = Divisors[n])*(-1)^(Range[Length[d], 1, -1])); Array[a, 100] (* Amiram Eldar, Mar 11 2020 *)
Table[Total[Times@@@Partition[Riffle[Reverse[Divisors[n]], {1, -1}, {2, -1, 2}], 2]], {n, 80}] (* Harvey P. Dale, Nov 06 2022 *)
PROG
(PARI) a(n) = my(d=Vecrev(divisors(n))); sum(k=1, #d, (-1)^(k+1)*d[k]); \\ Michel Marcus, Aug 11 2018
(APL, Dyalog dialect)
divisors ← {⍺←⍵{(0=⍵|⍺)/⍵}⍳⌊⍵*÷2 ⋄ 1=⍵:⍺ ⋄ ⍺, (⍵∘÷)¨(⍵=(⌊⍵*÷2)*2)↓⌽⍺}
A071324 ← {-/⌽(divisors ⍵)} ⍝ Antti Karttunen, Feb 16 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 18 2002, Jul 03 2008
STATUS
approved