cp's OEIS Frontend

A346250 Sum of -A252748 and its Dirichlet inverse.

%I A346250 #9 Jul 20 2021 10:45:40
%S A346250 2,0,0,1,0,2,0,-3,1,6,0,-11,0,6,6,-17,0,-23,0,-17,6,18,0,-39,9,18,-15,
%T A346250 -25,0,-48,0,-51,18,30,18,-49,0,30,18,-77,0,-72,0,-35,-61,34,0,-85,9,
%U A346250 -31,30,-43,0,-123,54,-97,30,54,0,-117,0,50,-77,-89,54,-96,0,-53,34,-104,0,-19,0,66,-55,-61,54,-120,0
%N A346250 Sum of -A252748 and its Dirichlet inverse.
%H A346250 Antti Karttunen, <a href="/A346250/b346250.txt">Table of n, a(n) for n = 1..16384</a>
%H A346250 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A346250 a(n) = A346248(n) - A252748(n).
%o A346250 (PARI)
%o A346250 up_to = 16384;
%o A346250 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 A346250 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A346250 A252748(n) = (A003961(n) - (2*n));
%o A346250 v346248 = DirInverseCorrect(vector(up_to,n,-A252748(n)));
%o A346250 A346248(n) = v346248[n];
%o A346250 A346250(n) = (A346248(n)-A252748(n));
%Y A346250 Cf. A003961, A252748, A346248.
%Y A346250 Cf. also A323911, A346236, A346247, A346255.
%K A346250 sign
%O A346250 1,1
%A A346250 _Antti Karttunen_, Jul 19 2021