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A355829
Dirichlet inverse of A009194, the greatest common divisor of sigma(n) and n, where sigma is the sum of divisors function.
2
1, -1, -1, 0, -1, -4, -1, 0, 0, 0, -1, 7, -1, 0, -1, 0, -1, 8, -1, 1, 1, 0, -1, -10, 0, 0, 0, -25, -1, 10, -1, 0, -1, 0, 1, 15, -1, 0, 1, -8, -1, 6, -1, -1, 2, 0, -1, 16, 0, 2, -1, 1, -1, -6, 1, 46, 1, 0, -1, -9, -1, 0, 0, 0, 1, 10, -1, 1, -1, 2, -1, -29, -1, 0, 4, -1, 1, 6, -1, 16, 0, 0, -1, 29, 1, 0, -1, 2, -1, -8
OFFSET
1,6
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A009194(n/d) * a(d).
MATHEMATICA
s[n_] := GCD[n, DivisorSigma[1, n]]; a[1] = 1; a[n_] := - DivisorSum[n, a[#] * s[n/#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Jul 20 2022 *)
PROG
(PARI)
A009194(n) = gcd(n, sigma(n));
memoA355829 = Map();
A355829(n) = if(1==n, 1, my(v); if(mapisdefined(memoA355829, n, &v), v, v = -sumdiv(n, d, if(d<n, A009194(n/d)*A355829(d), 0)); mapput(memoA355829, n, v); (v)));
CROSSREFS
Cf. also A355828.
Sequence in context: A127560 A098172 A049759 * A265421 A137252 A228623
KEYWORD
sign
AUTHOR
Antti Karttunen, Jul 20 2022
STATUS
approved