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%I #9 Feb 17 2021 20:26:27
%S 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 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 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 Number of prime factors (with multiplicity) shared by A003961(n) and A003973(n): a(n) = bigomega(gcd(A003961(n), sigma(A003961(n)))).
%H Antti Karttunen, <a href="/A341519/b341519.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = A001222(A336850(n)) = A001222(gcd(A003961(n), A003973(n))).
%F a(n) = A341523(A003961(n)).
%t 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 (PARI)
%o A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A341519(n) = bigomega(gcd(A003961(n), sigma(A003961(n))));
%Y Cf. A000203, A001222, A003961, A003973, A336850, A341523.
%K nonn
%O 1,24
%A _Antti Karttunen_, Feb 17 2021
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