A354825 - OEIS

A354825

Dirichlet inverse of A293442, where A293442 is multiplicative with a(p^e) = A019565(e).

1, -2, -2, 1, -2, 4, -2, -2, 1, 4, -2, -2, -2, 4, 4, 8, -2, -2, -2, -2, 4, 4, -2, 4, 1, 4, -2, -2, -2, -8, -2, -16, 4, 4, 4, 1, -2, 4, 4, 4, -2, -8, -2, -2, -2, 4, -2, -16, 1, -2, 4, -2, -2, 4, 4, 4, 4, 4, -2, 4, -2, 4, -2, 20, 4, -8, -2, -2, 4, -8, -2, -2, -2, 4, -2, -2, 4, -8, -2, -16, 8, 4, -2, 4, 4, 4, 4, 4

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OFFSET

1,2

COMMENTS

Multiplicative because A293442 is.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

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} A293442(n/d) * a(d).

PROG

(PARI)

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

A293442(n) = factorback(apply(e -> A019565(e), factor(n)[, 2]));

memoA354825 = Map();

A354825(n) = if(1==n, 1, my(v); if(mapisdefined(memoA354825, n, &v), v, v = -sumdiv(n, d, if(d<n, A293442(n/d)*A354825(d), 0)); mapput(memoA354825, n, v); (v)));

CROSSREFS

Cf. A019565, A293442.

Sequence in context: A369307 A366308 A347089 * A210531 A066954 A144925

Adjacent sequences: A354822 A354823 A354824 * A354826 A354827 A354828

KEYWORD

sign,mult

AUTHOR

Antti Karttunen, Jun 09 2022

STATUS

approved