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A354825
Dirichlet inverse of A293442, where A293442 is multiplicative with a(p^e) = A019565(e).
1
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
OFFSET
1,2
COMMENTS
Multiplicative because A293442 is.
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
Sequence in context: A369307 A366308 A347089 * A210531 A066954 A144925
KEYWORD
sign,mult
AUTHOR
Antti Karttunen, Jun 09 2022
STATUS
approved