This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378607 #13 Jan 13 2025 01:33:28
%S A378607 1,0,-1,-2,-1,0,-3,-6,-7,0,-1,2,-3,0,1,-14,-1,0,-3,2,3,0,-5,6,-11,0,
%T A378607 -25,6,-1,0,-5,-30,1,0,3,14,-3,0,3,6,-1,0,-3,2,7,0,-5,14,-31,0,1,6,-5,
%U A378607 0,1,18,3,0,-1,-2,-5,0,21,-62,3,0,-3,2,5,0,-1,42,-5,0,11,6,3,0,-3,14,-79,0,-5,-6,1,0,1,6,-7,0,9,10
%N A378607 Dirichlet convolution of sigma and the Dirichlet inverse of A003961 (A346234).
%H A378607 Antti Karttunen, <a href="/A378607/b378607.txt">Table of n, a(n) for n = 1..20000</a>
%H A378607 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A378607 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A378607 a(n) = Sum_{d|n} A000203(d)*A346234(n/d).
%F A378607 a(n) = Sum_{d|n} A349388(d).
%F A378607 Multiplicative with a(p^e) = (p^(e+1) - nextprime(p)*(p^e-1) - 1)/(p-1), where nextprime(p) = A151800(p). - _Amiram Eldar_, Jan 12 2025
%t A378607 f[p_, e_] := (p^(e + 1) - NextPrime[p]*(p^e - 1) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jan 12 2025 *)
%o A378607 (PARI)
%o A378607 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A378607 A346234(n) = (moebius(n)*A003961(n));
%o A378607 A378607(n) = sumdiv(n,d,sigma(d)*A346234(n/d));
%Y A378607 Cf. A000203, A003961, A016825, A151800, A346234, A378606 (Dirichlet inverse).
%Y A378607 Inverse Möbius transform of A349388.
%K A378607 sign,mult
%O A378607 1,4
%A A378607 _Antti Karttunen_, Dec 11 2024