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A359795
Dirichlet inverse of function f(n) = 1 + A048675(n), where A048675(n) is fully additive with a(p) = 2^(1-PrimePi(p)).
1
1, -2, -3, 1, -5, 8, -9, 0, 4, 14, -17, -7, -33, 26, 23, 0, -65, -16, -129, -13, 43, 50, -257, 2, 16, 98, -4, -25, -513, -84, -1025, 0, 83, 194, 77, 24, -2049, 386, 163, 4, -4097, -160, -8193, -49, -52, 770, -16385, 0, 64, -64, 323, -97, -32769, 24, 149, 8, 643, 1538, -65537, 115, -131073, 3074, -100
OFFSET
1,2
COMMENTS
Conjecture: the only odd term that occurs more than once is 1 = a(1) = a(4).
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} (1+A048675(n/d)) * a(d).
For n >= 1, a(3^2n) = 4 and a(3^(2n+1)) = -4.
PROG
(PARI)
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
memoA359795 = Map();
A359795(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359795, n, &v), v, v = -sumdiv(n, d, if(d<n, (1+A048675(n/d))*A359795(d), 0)); mapput(memoA359795, n, v); (v)));
CROSSREFS
Cf. A000720, A048675, A091428 (positions of odd terms), A359592 (parity of terms).
Sequence in context: A242108 A238941 A247582 * A224652 A271497 A293287
KEYWORD
sign
AUTHOR
Antti Karttunen, Jan 26 2023
STATUS
approved