A349357 - OEIS

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A349357

a(n) = A349355(n) + A349356(n).

2, 0, 0, 4, 0, 8, 0, 16, 4, 8, 0, 16, 0, 8, 8, 52, 0, 24, 0, 16, 8, 8, 0, 40, 4, 8, 24, 16, 0, 0, 0, 160, 8, 8, 8, 56, 0, 8, 8, 40, 0, 0, 0, 16, 24, 8, 0, 112, 4, 40, 8, 16, 0, 80, 8, 40, 8, 8, 0, 16, 0, 8, 24, 484, 8, 0, 0, 16, 8, 0, 0, 152, 0, 8, 40, 16, 8, 0, 0, 112, 112, 8, 0, 16, 8, 8, 8, 40, 0, 16, 8, 16

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OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

FORMULA

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A349355(d) * A349356(n/d). [As the sequences are Dirichlet inverses of each other]

MATHEMATICA

f1[p_, e_] := -2*(p - 1)^(e - 1); f2[p_, e_] := 2*(p + 1)^(e - 1); a[1] = 2; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) + Times @@ f2 @@@ f; Array[a, 100] (* Amiram Eldar, Nov 16 2021 *)

PROG

(PARI) A349357(n) = (A349355(n)+A349356(n)); \\ Needs also code from A349355 and A349356.

CROSSREFS

Cf. A003958, A003959, A063441, A097945, A349355, A349356.

Sequence in context: A349347 A354187 A349345 * A071390 A354350 A323884

Adjacent sequences: A349354 A349355 A349356 * A349358 A349359 A349360

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 16 2021

STATUS

approved