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A349359
Sum of A064216 and its Dirichlet inverse, where A064216 = A064989(2n-1), and A064989 is fully multiplicative with a(2) = 1 and a(p) = prevprime(p) for odd primes p.
2
2, 0, 0, 4, 0, 12, 0, 12, 9, 16, 0, 22, 0, 44, 24, 5, 0, 40, 0, 60, 66, 40, 0, 14, 16, 36, 51, 10, 0, 106, 0, 82, 60, 56, 88, 26, 0, 124, 54, -10, 0, -46, 0, 144, 134, 48, 0, 235, 121, 140, 84, 86, 0, 19, 80, -108, 186, 136, 0, -44, 0, 236, 211, 29, 72, 158, 0, 216, 72, 62, 0, 152, 0, 284, 190, 10, 220, 98, 0, 260, 181
OFFSET
1,1
COMMENTS
Compare to A323894 which in contrast to this sequence seems to have only nonnegative terms.
FORMULA
a(n) = A064216(n) + A349358(n).
a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1<d<n} A064216(d) * A349358(n/d).
PROG
(PARI)
A064989(n) = { my(f = factor(n)); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A064216(n) = A064989((2*n)-1);
memoA349358 = Map();
A349358(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349358, n, &v), v, v = -sumdiv(n, d, if(d<n, A064216(n/d)*A349358(d), 0)); mapput(memoA349358, n, v); (v)));
A349359(n) = (A064216(n)+A349358(n));
CROSSREFS
Cf. also A323894, A349126.
Sequence in context: A061669 A324641 A365804 * A323894 A349383 A359428
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 17 2021
STATUS
approved