

A058359


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


1



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
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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 A110332 A052947
Adjacent sequences: A058356 A058357 A058358 * A058360 A058361 A058362


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Dec 16 2000


STATUS

approved



