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 A349382 #12 Nov 26 2021 07:50:18
%S A349382 1,-2,-3,-2,-4,6,-6,-2,-6,8,-6,6,-6,12,12,-2,-6,12,-6,8,18,12,-10,6,
%T A349382 -12,12,-12,12,-8,-24,-8,-2,18,12,24,12,-10,12,18,8,-6,-36,-6,12,24,
%U A349382 20,-10,6,-30,24,18,12,-12,24,24,12,18,16,-8,-24,-8,16,36,-2,24,-36,-10,12,30,-48,-6,12,-8,20,36,12,36,-36
%N A349382 Dirichlet convolution of A064989 with A346234 (Dirichlet inverse of A003961), where A003961 and A064989 are fully multiplicative sequences that shift the prime factorization of n one step towards larger and smaller primes respectively.
%C A349382 Multiplicative because both A064989 and A346234 are.
%H A349382 Antti Karttunen, <a href="/A349382/b349382.txt">Table of n, a(n) for n = 1..20000</a>
%H A349382 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A349382 a(n) = Sum_{d|n} A064989(n/d) * A346234(d).
%F A349382 a(n) = A349383(n) - A349381(n).
%F A349382 Multiplicative with a(p^e) = -2 if p = 2, and prevprime(p)^e - nextprime(p) * prevprime(p)^(e-1) otherwise, where prevprime function is A151799 and nextprime function is A151800. - _Amiram Eldar_, Nov 17 2021
%t A349382 f[p_, e_] := If[p == 2, -2, NextPrime[p, -1]^e - NextPrime[p]*NextPrime[p, -1]^(e - 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 17 2021 *)
%o A349382 (PARI)
%o A349382 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A349382 A064989(n) = { my(f = factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A349382 A346234(n) = (moebius(n)*A003961(n));
%o A349382 A349382(n) = sumdiv(n,d,A064989(n/d)*A346234(d));
%Y A349382 Cf. A003961, A064989, A151799, A151800, A346234, A349381 (Dirichlet inverse), A349383 (sum with it).
%Y A349382 Cf. also A349355, A349356.
%K A349382 sign,mult
%O A349382 1,2
%A A349382 _Antti Karttunen_, Nov 17 2021