A346255 Sum of A336849 and its Dirichlet inverse.

2, 0, 0, 9, 0, 30, 0, 27, 25, 42, 0, -15, 0, 66, 70, 81, 0, -25, 0, 63, 110, 78, 0, 45, 49, 102, 125, -33, 0, -140, 0, 243, 130, 114, 154, 625, 0, 138, 170, 189, 0, -440, 0, 117, 175, 174, 0, -81, 121, 147, 190, -51, 0, 625, 182, 99, 230, 186, 0, 315, 0, 222, 275, 729, 238, -260, 0, 171, 290, -308, 0, 15, 0, 246, 245, -69, 286

Offset

1,1

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A336849(n) + A346254(n).

Prog

(PARI)
up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A336849(n) = { my(u=A003961(n)); (u/gcd(u, sigma(u))); };
v346254 = DirInverseCorrect(vector(up_to, n, A336849(n)));
A346254(n) = v346254[n];
A346255(n) = (A336849(n)+A346254(n));

Crossrefs

Cf. A000203, A003961, A003973, A336849, A346254.

Cf. also A346236, A346247, A346250.

Sequence in context: A347091 A347229 A347095 * A346480 A323399 A246714

Adjacent sequences: A346252 A346253 A346254 * A346256 A346257 A346258

Keyword

sign

Author

Antti Karttunen, Jul 19 2021

Status

approved