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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 18:46 EDT 2021. Contains 345419 sequences. (Running on oeis4.)