A329618 - OEIS

%I #13 Nov 18 2019 22:03:52

%S 1,1,1,2,1,2,1,1,2,2,1,1,1,2,2,4,1,1,1,1,2,2,1,4,2,2,1,1,1,3,1,1,2,2,

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

%U 2,1,1,1,1,2,1,1,2,3,1,1,4,2,1,4,2,2,2,4,1,4,2,1,2,2,2,2,1,1,3,4,1,3,1,4,1

%N a(n) = gcd(A001222(n), A324888(n)), where A324888(n) is the minimal number of primorials (A002110) that add to A108951(n).

%H Antti Karttunen, <a href="/A329618/b329618.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(A001222(n), A324888(n)) = gcd(A001222(n), A001222(A324886(n))).

%t With[{b = Reverse@ Prime@ Range@ 120}, Array[GCD[PrimeOmega@ #1, Total@ IntegerDigits[#2, MixedRadix[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)

%o 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 A324886(n) = A276086(A108951(n));

%o A329618(n) = gcd(bigomega(n), bigomega(A324886(n)));

%Y Cf. A001222, A034386, A108951, A276086, A324886, A324888, A329619, A329620, A329621.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 18 2019