A058359 Absolute value of difference between the even and odd first differences of the divisors of n.

0, 1, 2, 1, 4, 5, 6, 5, 8, 9, 10, 5, 12, 13, 14, 13, 16, 17, 18, 5, 20, 21, 22, 17, 24, 25, 26, 5, 28, 17, 30, 29, 32, 33, 34, 17, 36, 37, 38, 29, 40, 41, 42, 5, 44, 45, 46, 41, 48, 49, 50, 5, 52, 53, 54, 45, 56, 57, 58, 33, 60, 61, 62, 61, 64, 65, 66, 5, 68, 57, 70, 57, 72, 73, 74

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The divisors of twelve are {1, 2, 3, 4, 6 and 12}, the first difference is {1, 1, 1, 2 and 6}. The even differences add up to 8 while the odd differences add up to 3. The absolute difference between the even and odd first differences of 12 therefore is 5.

Maple

f:= proc(n) local Q, evens, odds;
  Q:= sort(convert(numtheory:-divisors(n), list));
  evens, odds:= selectremove(type, Q[2..-1]-Q[1..-2], even);
  abs(convert(evens, `+`)-convert(odds, `+`))
end proc:
map(f, [$1..100]); # Robert Israel, Jul 05 2016

Mathematica

f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; s = 0; i = 1; While[ i < l, e = d[ [ i + 1 ] ] - d[ [ i ] ]; If[ EvenQ[ e ], s = s + e, s = s - e ]; i++ ]; Abs[ s ]); Table[ f[ n ], {n, 1, 75} ]
avd[n_]:=Module[{d=Differences[Divisors[n]]}, Abs[Total[Select[d, OddQ]]-Total[ Select[ d, EvenQ]]]]; Array[avd, 80] (* Harvey P. Dale, Dec 31 2018 *)

Crossrefs

Sequence in context: A323456 A326058 A262586 * A261608 A351250 A351253

Adjacent sequences: A058356 A058357 A058358 * A058360 A058361 A058362

Keyword

nonn

Author

Robert G. Wilson v, Dec 16 2000

Status

approved