A366292 Dirichlet inverse of A353271, where A353271(n) is the numerator of n / A005940(1+(3*A156552(n))).

1, -1, -1, -1, -1, -1, -1, -1, -2, -3, -1, 1, -1, -5, -3, -1, -1, 0, -1, 9, -5, -9, -1, 11, -4, -11, -4, 13, -1, 5, -1, -1, -9, -15, -5, 6, -1, -17, -11, 5, -1, 21, -1, 21, -2, -21, -1, 5, -6, -8, -15, 25, -1, 22, -9, 7, -17, -27, -1, 3, -1, -29, 14, -1, -11, 11, -1, 33, -21, -3, -1, 16, -1, -35, -8, 37, -9, 13

Offset

1,9

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A353271(n/d) * a(d).

Prog

(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A332449(n) = A005940(1+(3*A156552(n)));
A353271(n) = (n / gcd(n, A332449(n)));
memoA366292 = Map();
A366292(n) = if(1==n, 1, my(v); if(mapisdefined(memoA366292, n, &v), v, v = -sumdiv(n, d, if(d<n, A353271(n/d)*A366292(d), 0)); mapput(memoA366292, n, v); (v)));

Crossrefs

Cf. A332449, A353271.

Cf. A038838 (positions of even terms), A122132 (of odd terms), A353627 (parity of terms).

Cf. also A209635, A342417, A354347, A354823, A359432, A359433, A359577 for other sequences that are equal modulo 2.

Sequence in context: A108756 A106178 A305807 * A205104 A215561 A108714

Adjacent sequences: A366289 A366290 A366291 * A366293 A366294 A366295

Keyword

sign

Author

Antti Karttunen, Oct 06 2023

Status

approved