

A071324


Alternating sum of all divisors of n; divisors nonincreasing, starting with n.


22



1, 1, 2, 3, 4, 4, 6, 5, 7, 6, 10, 8, 12, 8, 12, 11, 16, 13, 18, 12, 16, 12, 22, 16, 21, 14, 20, 18, 28, 22, 30, 21, 24, 18, 32, 25, 36, 20, 28, 24, 40, 32, 42, 30, 36, 24, 46, 32, 43, 31, 36, 36, 52, 40, 48, 38, 40, 30, 58, 40, 60, 32, 46, 43, 56, 48, 66, 48, 48, 42, 70, 49, 72
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OFFSET

1,3


COMMENTS

a(A028983(n)) mod 2 = 0; a(A028982(n)) mod 2 = 1.


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


EXAMPLE

Divisors of 20: {1,2,4,5,10,20} therefore a(20) = 20  10 + 5  4 + 2  1 = 12.


MATHEMATICA

a[n_] := Plus @@ ((d = Divisors[n])*(1)^(Range[Length[d], 1, 1])); Array[a, 100] (* Amiram Eldar, Mar 11 2020 *)


PROG

(PARI) a(n) = my(d=Vecrev(divisors(n))); sum(k=1, #d, (1)^(k+1)*d[k]); \\ Michel Marcus, Aug 11 2018


CROSSREFS

Cf. A000203, A071322, a(n) = abs(A071323(n)).
Cf. A134871.
Sequence in context: A228286 A158973 A071323 * A321441 A063655 A111234
Adjacent sequences: A071321 A071322 A071323 * A071325 A071326 A071327


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, May 18 2002, Jul 03 2008


STATUS

approved



