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 A342417 Dirichlet inverse of A342002. 4

%I

%S 1,-1,-5,-1,-7,9,-7,-5,-6,1,-41,5,-9,3,33,-1,-47,-6,-11,19,27,63,-53,

%T 41,36,1,136,7,-59,7,-9,25,369,77,43,16,-59,-49,-157,-9,-317,-19,-73,

%U -13,-10,-21,-359,-53,-38,-52,139,-105,-401,-348,473,-23,-263,-51,-443,-201,-11,5,292,23,65,-893,-69,-5,253,31

%N Dirichlet inverse of A342002.

%H Antti Karttunen, <a href="/A342417/b342417.txt">Table of n, a(n) for n = 1..11550</a>

%o (PARI)

%o up_to = 11550;

%o 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.

%o 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); };

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

%o A342417(n) = v342417[n];

%Y Cf. A342002, A342419.

%K sign

%O 1,3

%A _Antti Karttunen_, Mar 13 2021

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Last modified January 22 21:47 EST 2022. Contains 350504 sequences. (Running on oeis4.)