A366292 - OEIS

%I #11 Oct 06 2023 21:22:52

%S 1,-1,-1,-1,-1,-1,-1,-1,-2,-3,-1,1,-1,-5,-3,-1,-1,0,-1,9,-5,-9,-1,11,

%T -4,-11,-4,13,-1,5,-1,-1,-9,-15,-5,6,-1,-17,-11,5,-1,21,-1,21,-2,-21,

%U -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

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

%H Antti Karttunen, <a href="/A366292/b366292.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o 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 };

%o A332449(n) = A005940(1+(3*A156552(n)));

%o A353271(n) = (n / gcd(n, A332449(n)));

%o memoA366292 = Map();

%o 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)));

%Y Cf. A332449, A353271.

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

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

%K sign

%O 1,9

%A _Antti Karttunen_, Oct 06 2023