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A329484 Dirichlet convolution of the Louiville function with itself. 0
1, -2, -2, 3, -2, 4, -2, -4, 3, 4, -2, -6, -2, 4, 4, 5, -2, -6, -2, -6, 4, 4, -2, 8, 3, 4, -4, -6, -2, -8, -2, -6, 4, 4, 4, 9, -2, 4, 4, 8, -2, -8, -2, -6, -6, 4, -2, -10, 3, -6, 4, -6, -2, 8, 4, 8, 4, 4, -2, 12, -2, 4, -6, 7, 4, -8, -2, -6, 4, -8, -2, -12, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Up to sign this sequence partitions the positive integers in the same way as A008836. Additional interesting partitions exist when values of this sequence are taken into account.

LINKS

Table of n, a(n) for n=1..73.

Wikipedia, Liouville function

Eric Weisstein's World of Mathematics, Liouville Function

FORMULA

a(n) = Sum{d|n} A008836(d) * A008836(n/d).

MATHEMATICA

a[n_] := DivisorSum[n, LiouvilleLambda[#] * LiouvilleLambda[n/#] &] ; Array[a, 100] (* Amiram Eldar, Jan 18 2020 *)

PROG

(PARI) a(n) = sumdiv(n, d, (-1)^bigomega(d) * (-1)^bigomega(n/d))

CROSSREFS

Cf. A008836.

Sequence in context: A167447 A134687 A184395 * A179941 A179942 A000005

Adjacent sequences:  A329481 A329482 A329483 * A329485 A329487 A329488

KEYWORD

sign

AUTHOR

Torlach Rush, Jan 17 2020

STATUS

approved

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Last modified February 23 21:20 EST 2020. Contains 332195 sequences. (Running on oeis4.)