A354826 - OEIS

A354826

Dirichlet inverse of A238745.

1, -2, -2, 0, -2, 5, -2, 0, 0, 5, -2, -2, -2, 5, 5, 0, -2, -2, -2, -2, 5, 5, -2, 0, 0, 5, 0, -2, -2, -17, -2, 0, 5, 5, 5, 8, -2, 5, 5, 0, -2, -17, -2, -2, -2, 5, -2, 0, 0, -2, 5, -2, -2, 0, 5, 0, 5, 5, -2, 16, -2, 5, -2, 0, 5, -17, -2, -2, 5, -17, -2, -8, -2, 5, -2, -2, 5, -17, -2, 0, 0, 5, -2, 16, 5, 5, 5, 0, -2, 16

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..12600

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

FORMULA

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A238745(n/d) * a(d).

PROG

(PARI)

A124859(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = prod(j=1, f[k, 2], prime(j)); f[k, 2] = 1); factorback(f); }; \\ From A124859

A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));

A238745(n) = A181819(A124859(n));

memoA354826 = Map();

A354826(n) = if(1==n, 1, my(v); if(mapisdefined(memoA354826, n, &v), v, v = -sumdiv(n, d, if(d<n, A238745(n/d)*A354826(d), 0)); mapput(memoA354826, n, v); (v)));

CROSSREFS

Cf. A238745.

Cf. also A354349, A354359.

Sequence in context: A278483 A008281 A094671 * A202015 A193350 A021458

Adjacent sequences: A354823 A354824 A354825 * A354827 A354828 A354829

KEYWORD

sign

AUTHOR

Antti Karttunen, Jun 09 2022

STATUS

approved