A103977 Let d_1 ... d_k be the divisors of n. Then a(n) = min_{ e_1 = +-1, ... e_k = +-1 } | Sum_i e_i d_i |.

1, 1, 2, 1, 4, 0, 6, 1, 5, 2, 10, 0, 12, 4, 6, 1, 16, 1, 18, 0, 10, 8, 22, 0, 19, 10, 14, 0, 28, 0, 30, 1, 18, 14, 22, 1, 36, 16, 22, 0, 40, 0, 42, 4, 12, 20, 46, 0, 41, 7, 30, 6, 52, 0, 38, 0, 34, 26, 58, 0, 60, 28, 22, 1, 46, 0, 66, 10, 42, 0, 70, 1, 72, 34, 26, 12, 58, 0, 78, 0

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

If n=p (prime), then a(n)=p-1. If n=2^m, then a(n)=1. [Corrected by R. J. Mathar, Nov 27 2007]

a(n) = 0 iff n is a Zumkeller number (A083207). - Amiram Eldar, Jan 05 2020

Example

a(6) = 1 + 2 + 3 - 6 = 0.

Maple

A103977 := proc(n) local divs, a, acandid, filt, i, p, sigs ; divs := convert(numtheory[divisors](n), list) ; a := add(i, i=divs) ; for sigs from 0 to 2^nops(divs)-1 do filt := convert(sigs, base, 2) ; while nops(filt) < nops(divs) do filt := [op(filt), 0] ; od ; acandid := 0 ; for p from 0 to nops(divs)-1 do if op(p+1, filt) = 0 then acandid := acandid-op(p+1, divs) ; else acandid := acandid+op(p+1, divs) ; fi ; od: acandid := abs(acandid) ; if acandid < a then a := acandid ; fi ; od: RETURN(a) ; end: seq(A103977(n), n=1..80) ; # R. J. Mathar, Nov 27 2007

Mathematica

a[n_] := Module[{d = Divisors[n], c, p, m}, c = CoefficientList[Product[1 + x^i, {i, d}], x]; p = -1 + Position[c, _?(# > 0 &)] // Flatten; m = Length[p]; If[OddQ[m], If[(d = p[[(m + 1)/2]] - p[[(m - 1)/2]]) == 1, 0, d], p[[m/2 + 1]] - p[[m/2]]]]; Array[a, 100] (* Amiram Eldar, Dec 11 2019 *)

Crossrefs

Cf. A125732, A125733, A005835, A023196, A083207.

Sequence in context: A326144 A120112 A233150 * A109883 A033880 A033879

Adjacent sequences: A103974 A103975 A103976 * A103978 A103979 A103980

Keyword

nonn

Author

Yasutoshi Kohmoto, Jan 01 2007

Extensions

More terms from R. J. Mathar, Nov 27 2007

Status

approved