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A358217 Number of prime factors (with multiplicity) in A319627(n).

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%I A358217 #10 Nov 05 2022 12:34:20
%S A358217 0,0,1,0,1,0,1,0,2,1,1,0,1,1,1,0,1,1,1,1,2,1,1,0,2,1,3,1,1,0,1,0,2,1,
%T A358217 1,0,1,1,2,1,1,1,1,1,2,1,1,0,2,2,2,1,1,2,2,1,2,1,1,0,1,1,3,0,2,1,1,1,
%U A358217 2,1,1,0,1,1,2,1,1,1,1,1,4,1,1,1,2,1,2,1,1,1,2,1,2,1,2,0,1,2,3,2,1,1,1,1,1,1,1,1,1,2,2,1,1,1,2,1,3,1,2,0
%N A358217 Number of prime factors (with multiplicity) in A319627(n).
%H A358217 Antti Karttunen, <a href="/A358217/b358217.txt">Table of n, a(n) for n = 1..65537</a>
%H A358217 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A358217 a(n) = A001222(A319627(n)).
%F A358217 Apparently, a(n) <= A358218(n) for all n.
%o A358217 (PARI)
%o A358217 A064989(n) = {my(f); 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 A358217 A319627(n) = (A064989(n) / gcd(n, A064989(n)));
%o A358217 A358217(n) = bigomega(A319627(n));
%Y A358217 Cf. A001222, A025487 (positions of zeros), A064989, A319627,
%Y A358217 Cf. A358219 (positions where differs from A358218).
%K A358217 nonn
%O A358217 1,9
%A A358217 _Antti Karttunen_, Nov 04 2022