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A342419 Sum of A342002 and its Dirichlet inverse. 3
2, 0, 0, 1, 0, 10, 0, 3, 25, 14, 0, 7, 0, 14, 70, 15, 0, -3, 0, 33, 70, 82, 0, 45, 49, 18, 185, 29, 0, 8, 0, 35, 410, 94, 98, 28, 0, 22, 90, 97, 0, 0, 0, 79, 279, 106, 0, -27, 49, 61, 470, 43, 0, -315, 574, 111, 110, 118, 0, -199, 0, 18, 339, 43, 126, -876, 0, 81, 530, 152, 0, 6, 0, 118, -87, 153, 574, 412, 0, 267 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Zeros occurring on composite n are rare: 42 and 4718 are the first two such positions.

It seems that many nonzero squares occur on square n.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..11550

FORMULA

a(n) = A342002(n) + A342417(n).

PROG

(PARI)

up_to = 11550;

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.

A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };

v342417 = DirInverseCorrect(vector(up_to, n, A342002(n)));

A342417(n) = v342417[n];

A342419(n) = (A342002(n)+A342417(n));

CROSSREFS

Cf. A342002, A342417.

Sequence in context: A335156 A158785 A346243 * A226350 A112609 A134363

Adjacent sequences:  A342416 A342417 A342418 * A342420 A342421 A342422

KEYWORD

sign

AUTHOR

Antti Karttunen, Mar 13 2021

STATUS

approved

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)