login
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, -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
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. 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
KEYWORD
sign
AUTHOR
Antti Karttunen, Oct 06 2023
STATUS
approved