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A359433
Dirichlet inverse of A071773.
4
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
OFFSET
1,9
COMMENTS
Multiplicative because A071773 is.
LINKS
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
KEYWORD
sign,mult
AUTHOR
Antti Karttunen, Jan 02 2023
STATUS
approved