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A356154
Dirichlet inverse of A356153.
2
1, -1, -2, 0, -1, 3, -1, 0, 3, 1, -1, -1, -1, 1, 3, 0, -1, -7, -1, -1, 2, 1, -1, 0, -1, 1, -5, 0, -1, -5, -1, 0, 3, 1, 1, 5, -1, 1, 2, 2, -1, -3, -1, 0, -7, 1, -1, 0, -4, 2, 3, 0, -1, 15, 1, -3, 2, 1, -1, 5, -1, 1, -3, 0, 1, -5, -1, 0, 3, -1, -1, -2, -1, 1, 2, 0, -1, -3, -1, -1, 8, 1, -1, 1, 1, 1, 3, 0, -1, 17
OFFSET
1,3
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A356153(n/d) * a(d).
PROG
(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A356153(n) = for(k=1, oo, if((k*A276086(k))%n==0, return(k/gcd(n, k))));
memoA356154 = Map();
A356154(n) = if(1==n, 1, my(v); if(mapisdefined(memoA356154, n, &v), v, v = -sumdiv(n, d, if(d<n, A356153(n/d)*A356154(d), 0)); mapput(memoA356154, n, v); (v)));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Jul 28 2022
STATUS
approved