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)).

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, 15, 30, 15, 30, 7, 14, 21, 42, 21, 42, 35, 70, 105, 210, 105, 210, 35, 70, 105, 210, 105, 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

Offset: 0

Author

Antti Karttunen, Oct 20 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768
• Index entries for sequences related to primorial base

Crossrefs

Cf. A001221, A007947, A083346, A267263, A276086, A328572.

Cf. A276156 (gives the indices where this coincides with A276086).

Programs

Mathematica

rad[n_] := Times @@ FactorInteger[n][[All, 1]];
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];
a[n_] := rad[A276086[n]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 01 2021, after Antti Karttunen in A276086 *)

PARI

A328571(n) = { my(m=1, p=2); while(n, m *= (p^!!(n%p)); n = n\p; p = nextprime(1+p)); (m); };

Formula

a(n) = A007947(A276086(n)).

a(n) = A276086(n) / A328572(n).

a(A276156(n)) = A276086(A276156(n)). [And at no other points the equality holds]

A001221(a(n)) = A267263(n).

a(n) = A083346(A276086(n)). - Antti Karttunen, Feb 28 2021