A359433 - OEIS

A359433

Dirichlet inverse of A071773.

1, -1, -1, -1, -1, 1, -1, 1, -2, 1, -1, 1, -1, 1, 1, 1, -1, 2, -1, 1, 1, 1, -1, -1, -4, 1, 2, 1, -1, -1, -1, -1, 1, 1, 1, 2, -1, 1, 1, -1, -1, -1, -1, 1, 2, 1, -1, -1, -6, 4, 1, 1, -1, -2, 1, -1, 1, 1, -1, -1, -1, 1, 2, -1, 1, -1, -1, 1, 1, -1, -1, -2, -1, 1, 4, 1, 1, -1, -1, -1, 4, 1, -1, -1, 1, 1, 1, -1, -1, -2, 1, 1, 1, 1, 1, 1, -1, 6, 2, 4, -1, -1, -1, -1, -1

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OFFSET

1,9

COMMENTS

Multiplicative because A071773 is.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

Multiplicative with a(p^e) = (-1)^e * (1-p)^floor(e/2). - Sebastian Karlsson, Jan 03 2023

MATHEMATICA

f[p_, e_] := (-1)^e * (1-p)^Floor[e/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 04 2023 *)

PROG

(PARI)

A071773(n) = { my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]>1)); };

memoA359433 = Map();

A359433(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359433, n, &v), v, v = -sumdiv(n, d, if(d<n, A071773(n/d)*A359433(d), 0)); mapput(memoA359433, n, v); (v)));

CROSSREFS

Cf. A071773.

Cf. A038838 (positions of even terms), A122132 (of odd terms), A353627 (parity of terms).

Cf. also A359432.

Sequence in context: A298735 A055090 A290106 * A349340 A326297 A060128

Adjacent sequences: A359430 A359431 A359432 * A359434 A359435 A359436

KEYWORD

sign,mult

AUTHOR

Antti Karttunen, Jan 02 2023

STATUS

approved