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A347239 Sum of A347236 and its Dirichlet inverse. 3
2, 0, 0, 1, 0, 4, 0, 13, 4, 4, 0, 26, 0, 8, 8, 55, 0, 34, 0, 26, 16, 4, 0, 26, 4, 8, 68, 52, 0, 0, 0, 133, 8, 4, 16, 223, 0, 8, 16, 26, 0, 0, 0, 26, 68, 12, 0, 110, 16, 74, 8, 52, 0, 68, 8, 52, 16, 4, 0, 4, 0, 12, 136, 463, 16, 0, 0, 26, 24, 0, 0, 247, 0, 8, 148, 52, 16, 0, 0, 110, 421, 4, 0, 8, 8, 8, 8, 26, 0, 8, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It seems that A030059 gives the positions of all zeros.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

FORMULA

a(n) = A347236(n) + A347238(n).

a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1<d<n} A347236(d) * A347238(n/d).

For all n >= 1, a(A030059(n)) = 0 and a(A030229(n)) = 2*A347236(A030229(n)).

For all n >= 1, a(A001248(n)) = A000290(A001223(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); };

A061019(n) = (((-1)^bigomega(n))*n);

A347236(n) = sumdiv(n, d, A061019(d)*A003961(n/d));

v347238 = DirInverseCorrect(vector(up_to, n, A347236(n)));

A347238(n) = v347238[n];

A347239(n) = (A347236(n)+A347238(n));

CROSSREFS

Cf. A000290, A001223, A001248, A003961, A061019, A030059, A030229, A347236, A347238.

Sequence in context: A349389 A323408 A347099 * A347097 A339274 A335156

Adjacent sequences:  A347236 A347237 A347238 * A347240 A347241 A347242

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 24 2021

STATUS

approved

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Last modified January 18 17:18 EST 2022. Contains 350455 sequences. (Running on oeis4.)