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A369454
Dirichlet inverse of A369257, where A369257 is the number of divisors of n that are odd numbers with an even number of prime factors with multiplicity.
3
1, -1, -1, 0, -1, 1, -1, 0, -1, 1, -1, 0, -1, 1, 0, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, 0, 2, 1, -1, 0, -1, 1, 0, 0, -1, -1, 0, 0, 0, 1, -1, 0, -1, 1, 2, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 1, 2, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 1, 0, 0, -1, -2, 0, 0, 0, 1, 0, 0, -1, 1, 2, 0
OFFSET
1,45
LINKS
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A369257(n/d) * a(d).
PROG
(PARI)
A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
A369257(n) = sumdiv(n, d, A353557(d));
memoA369454 = Map();
A369454(n) = if(1==n, 1, my(v); if(mapisdefined(memoA369454, n, &v), v, v = -sumdiv(n, d, if(d<n, A369257(n/d)*A369454(d), 0)); mapput(memoA369454, n, v); (v)));
CROSSREFS
Cf. also A358777, A369454.
Sequence in context: A128409 A133699 A157361 * A224444 A101808 A145865
KEYWORD
sign
AUTHOR
Antti Karttunen, Jan 27 2024
STATUS
approved