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A378531
Dirichlet convolution of A378432 and A378542.
3
1, 0, 0, 2, 0, 3, 0, 2, 2, 3, 0, 4, 0, 3, 3, 6, 0, 4, 0, 4, 3, 3, 0, 14, 2, 3, 2, 4, 0, 6, 0, 10, 3, 3, 3, 18, 0, 3, 3, 14, 0, 6, 0, 4, 4, 3, 0, 30, 2, 4, 3, 4, 0, 14, 3, 14, 3, 3, 0, 30, 0, 3, 4, 22, 3, 6, 0, 4, 3, 6, 0, 48, 0, 3, 4, 4, 3, 6, 0, 30, 6, 3, 0, 30, 3, 3, 3, 14, 0, 30, 3, 4, 3, 3, 3, 74, 0, 4, 4, 18
OFFSET
1,4
COMMENTS
Möbius transform of A378533.
LINKS
FORMULA
a(n) = Sum_{d|n} A378432(d)*A378542(n/d).
a(n) = Sum_{d|n} A008683(d)*A378533(n/d).
PROG
(PARI)
A033879(n) = ((2*n)-sigma(n));
A296075(n) = sumdiv(n, d, A033879(d));
memoA378432 = Map();
A378432(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378432, n, &v), v, v = -sumdiv(n, d, if(d<n, A296075(n/d)*A378432(d), 0)); mapput(memoA378432, n, v); (v)));
A378542(n) = sumdiv(n, d, d*!(bigomega(n/d)%2));
A378531(n) = sumdiv(n, d, A378432(d)*A378542(n/d));
CROSSREFS
Cf. A008683, A378532 (Dirichlet inverse), A378432, A378533 (inverse Möbius transform), A378542.
Cf. also A345182.
Sequence in context: A355930 A229946 A378532 * A127460 A274021 A303711
KEYWORD
nonn,new
AUTHOR
Antti Karttunen, Dec 01 2024
STATUS
approved