cp's OEIS Frontend

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.

A341519 Number of prime factors (with multiplicity) shared by A003961(n) and A003973(n): a(n) = bigomega(gcd(A003961(n), sigma(A003961(n)))).

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%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