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A328571 Primorial base expansion of n converted into its prime product form, but with all nonzero digits replaced by 1's: a(n) = A007947(A276086(n)).

%I A328571 #21 Dec 01 2021 11:25:17
%S A328571 1,2,3,6,3,6,5,10,15,30,15,30,5,10,15,30,15,30,5,10,15,30,15,30,5,10,
%T A328571 15,30,15,30,7,14,21,42,21,42,35,70,105,210,105,210,35,70,105,210,105,
%U A328571 210,35,70,105,210,105,210,35,70,105,210,105,210,7,14,21,42,21,42,35,70,105,210,105,210,35,70,105,210,105,210,35,70
%N A328571 Primorial base expansion of n converted into its prime product form, but with all nonzero digits replaced by 1's: a(n) = A007947(A276086(n)).
%H A328571 Antti Karttunen, <a href="/A328571/b328571.txt">Table of n, a(n) for n = 0..32768</a>
%H A328571 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328571 a(n) = A007947(A276086(n)).
%F A328571 a(n) = A276086(n) / A328572(n).
%F A328571 a(A276156(n)) = A276086(A276156(n)). [And at no other points the equality holds]
%F A328571 A001221(a(n)) = A267263(n).
%F A328571 a(n) = A083346(A276086(n)). - _Antti Karttunen_, Feb 28 2021
%t A328571 rad[n_] := Times @@ FactorInteger[n][[All, 1]];
%t A328571 A276086[n0_] := Module[{m = 1, i = 1, n = n0, p}, While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; m];
%t A328571 a[n_] := rad[A276086[n]];
%t A328571 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Dec 01 2021, after _Antti Karttunen_ in A276086 *)
%o A328571 (PARI) A328571(n) = { my(m=1, p=2); while(n, m *= (p^!!(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%Y A328571 Cf. A001221, A007947, A083346, A267263, A276086, A328572.
%Y A328571 Cf. A276156 (gives the indices where this coincides with A276086).
%K A328571 nonn
%O A328571 0,2
%A A328571 _Antti Karttunen_, Oct 20 2019