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, 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.

Links

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

Index entries for sequences computed from indices in prime factorization

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. A064216, A064989, A349358.

Cf. also A323894, A349126.

Sequence in context: A061669 A324641 A365804 * A323894 A349383 A359428

Adjacent sequences: A349356 A349357 A349358 * A349360 A349361 A349362

Keyword

sign

Author

Antti Karttunen, Nov 17 2021

Status

approved