cp's OEIS Frontend

A346104 Dirichlet inverse of A342920.

%I A346104 #17 Jul 12 2021 18:00:36
%S A346104 1,-1,-1,-1,-1,0,-1,-5,-11,0,-1,1,-1,0,-4,-1,-1,1,-1,1,-4,0,-1,-8,-49,
%T A346104 0,7,1,-1,-48,-1,25,-4,0,-124,12,-1,0,-4,0,-1,-10,-1,1,-13,0,-1,41,
%U A346104 -1485,1,-4,1,-1,22,-92,10,-4,0,-1,76,-1,0,-39,23,-262,2,-1,1,-4,134,-1,-138,-1,0,-1033,1,-240,2,-1,11,-201,0,-1,6
%N A346104 Dirichlet inverse of A342920.
%C A346104 The lowermost scatter plot gives an appearance of an elliptic galaxy seen from its side.
%H A346104 Antti Karttunen, <a href="/A346104/b346104.txt">Table of n, a(n) for n = 1..10000</a>
%H A346104 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A346104 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A346104 (PARI)
%o A346104 up_to = 2310;
%o A346104 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 (correctly!)
%o A346104 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A346104 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A346104 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 A346104 A342920(n) = A342002(A108951(n));
%o A346104 v346104 = DirInverseCorrect(vector(up_to,n,A342920(n)));
%o A346104 A346104(n) = v346104[n];
%Y A346104 Cf. A108951, A324886, A342001, A342002, A342920, A346103.
%Y A346104 Cf. also A342417.
%K A346104 sign,look
%O A346104 1,8
%A A346104 _Antti Karttunen_, Jul 09 2021