A349340 - OEIS

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A349340

Dirichlet inverse of A003557, where A003557 is multiplicative with a(p^e) = p^(e-1).

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, -4, 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, 4, 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, -8, 1, -1, -1, 1, 1, 1, 1, -1, -2, 1

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OFFSET

1,9

LINKS

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

FORMULA

Multiplicative with a(p^e) = -((p-1)^(e-1)).

a(n) = A076479(n) * A326297(n).

a(1) = 1; a(n) = -Sum_{d|n, d < n} A003557(n/d) * a(d).

MATHEMATICA

f[p_, e_] := -(p - 1)^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 18 2021 *)

PROG

(PARI)

A003557(n) = (n/factorback(factorint(n)[, 1]));

memoA349340 = Map();

A349340(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349340, n, &v), v, v = -sumdiv(n, d, if(d<n, A003557(n/d)*A349340(d), 0)); mapput(memoA349340, n, v); (v)));

(PARI) A349340(n) = { my(f=factor(n)); prod(i=1, #f~, -((f[i, 1]-1)^(f[i, 2]-1))); };

CROSSREFS

Cf. A003557, A076479, A326297 (absolute values).

Cf. also A325126, A349350, A349619.

Sequence in context: A055090 A290106 A359433 * A326297 A060128 A330751

Adjacent sequences: A349337 A349338 A349339 * A349341 A349342 A349343

KEYWORD

sign,mult

AUTHOR

Antti Karttunen, Nov 18 2021

STATUS

approved