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 A341519 #9 Feb 17 2021 20:26:27 %S A341519 0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,2,0,1,0,1,0,1,0,0,0,0, %T A341519 0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,1,2,0,1,1,1,0,0,0,1,0,0,0,0,0,1,0,0, %U A341519 1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,2,0,1,0,0,0,0,0,1,0,1,0,1,0,0,0,1,0,2,0,2,0 %N A341519 Number of prime factors (with multiplicity) shared by A003961(n) and A003973(n): a(n) = bigomega(gcd(A003961(n), sigma(A003961(n)))). %H A341519 Antti Karttunen, <a href="/A341519/b341519.txt">Table of n, a(n) for n = 1..65537</a> %H A341519 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a> %H A341519 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a> %F A341519 a(n) = A001222(A336850(n)) = A001222(gcd(A003961(n), A003973(n))). %F A341519 a(n) = A341523(A003961(n)). %t A341519 f[p_, e_] := NextPrime[p]^e; g[1] = 1; g[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := PrimeOmega[GCD[(gn = g[n]), DivisorSigma[1, gn]]]; Array[a, 100] (* _Amiram Eldar_, Feb 17 2021 *) %o A341519 (PARI) %o A341519 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961 %o A341519 A341519(n) = bigomega(gcd(A003961(n), sigma(A003961(n)))); %Y A341519 Cf. A000203, A001222, A003961, A003973, A336850, A341523. %K A341519 nonn %O A341519 1,24 %A A341519 _Antti Karttunen_, Feb 17 2021