cp's OEIS Frontend

A346247 Sum of A344587 (the deficiency of prime shifted n) and its Dirichlet inverse.

%I A346247 #13 Jul 20 2021 10:46:09
%S A346247 2,0,0,4,0,16,0,12,16,24,0,16,0,40,48,37,0,28,0,28,80,48,0,36,36,64,
%T A346247 88,52,0,-48,0,114,96,72,120,54,0,88,128,68,0,-64,0,64,116,112,0,92,
%U A346247 100,68,144,88,0,124,144,132,176,120,0,-12,0,144,204,349,192,-72,0,100,224,-72,0,128,0,160,160,124,240,-88,0,182
%N A346247 Sum of A344587 (the deficiency of prime shifted n) and its Dirichlet inverse.
%H A346247 Antti Karttunen, <a href="/A346247/b346247.txt">Table of n, a(n) for n = 1..16383</a>
%H A346247 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A346247 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A346247 a(n) = A344587(n) + A346246(n).
%F A346247 a(n) = A323911(A003961(n)).
%o A346247 (PARI)
%o A346247 up_to = 16384;
%o A346247 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 A346247 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A346247 A344587(n) = { my(u=A003961(n)); (u+u - sigma(u)); };
%o A346247 v346246 = DirInverseCorrect(vector(up_to,n,A344587(n)));
%o A346247 A346246(n) = v346246[n];
%o A346247 A346247(n) = (A344587(n)+A346246(n));
%Y A346247 Cf. A000203, A003961, A323911, A344587, A346246.
%Y A346247 Cf. also A346250.
%K A346247 sign
%O A346247 1,1
%A A346247 _Antti Karttunen_, Jul 19 2021