%I #9 Nov 18 2019 22:04:31

%S 1,1,1,2,1,1,1,1,2,2,1,4,1,1,1,4,1,1,1,1,6,2,1,1,6,1,2,2,1,6,1,1,1,2,

%T 1,2,1,1,2,2,1,1,1,1,1,2,1,2,8,1,3,4,1,1,2,1,2,1,1,1,1,2,2,2,1,4,1,1,

%U 1,2,1,1,1,1,2,2,9,3,1,1,8,2,1,4,2,1,6,8,1,4,2,1,1,2,1,1,1,1,3,8,1,2,1,1,1

%N a(n) = gcd(A056239(n), A324888(n)) = gcd(A001222(A108951(n)), A001222(A324886(n))).

%H Antti Karttunen, <a href="/A329621/b329621.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/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = gcd(A056239(n), A324888(n)) = gcd(A001222(A108951(n)), A001222(A324886(n))).

%t With[{b = MixedRadix[Reverse@ Prime@ Range@ 500]}, Array[GCD @@ PrimeOmega@ {#, Function[k, Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ k, Reverse@ k}]@ IntegerDigits[#, b]} &@ Apply[Times, Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]] &, 105]] (* _Michael De Vlieger_, Nov 18 2019 *)

%o (PARI) A034386(n) = prod(i=1, primepi(n), prime(i));

%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A329621(n) = { my(u=A108951(n)); gcd(bigomega(u), bigomega(A276086(u))); };

%Y Cf. A001222, A034386, A056239, A108951, A276086, A324886, A324888, A329618, A329622.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 18 2019