A329621 a(n) = gcd(A056239(n), A324888(n)) = gcd(A001222(A108951(n)), A001222(A324886(n))).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Nov 18 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

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

Programs

Mathematica

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 *)

PARI

A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A329621(n) = { my(u=A108951(n)); gcd(bigomega(u), bigomega(A276086(u))); };

Formula

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