A349436 a(n) = A349434(n) + A349435(n).

2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 12

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} A349434(d) * A349435(n/d). [As the sequences are Dirichlet inverses of each other]

Mathematica

s[n_] := n * DivisorSum[n, 1/# &, !CompositeQ[#] &]; sinv[1] = 1; sinv[n_] := sinv[n] = -DivisorSum[n, sinv[#] * s[n/#] &, # < n &]; f[p_, e_] := e/p; d[1] = 1; d[n_] := n*(1 + Plus @@ f @@@ FactorInteger[n]); dinv[1] = 1; dinv[n_] := dinv[n] = -DivisorSum[n, dinv[#] * d[n/#] &, # < n &];  a[n_] := DivisorSum[n, dinv[#] * s[n/#] + sinv[#] * d[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 18 2021 *)

Prog

(PARI) A349436(n) = (A349434(n) + A349435(n)); \\ Needs also code from A349434 and A349435.

Crossrefs

Cf. A349434, A349435.

Sequence in context: A331918 A089803 A354449 * A089811 A091888 A083928

Adjacent sequences: A349433 A349434 A349435 * A349437 A349438 A349439

Keyword

sign

Author

Antti Karttunen, Nov 17 2021

Status

approved