A331596 - OEIS

%I #13 Jul 27 2024 23:17:04

%S 0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,2,1,1,2,1,

%T 2,1,1,1,2,1,1,2,1,1,2,1,1,1,1,2,2,1,1,1,2,1,2,1,1,1,1,1,2,1,2,2,1,1,

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

%N Number of distinct prime factors of gcd(A122111(n), A241909(n)).

%H Antti Karttunen, <a href="/A331596/b331596.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>

%F a(n) = A001221(A331596(n)) = A001221(gcd(A122111(n), A241909(n))).

%F a(n) = A001222(A331597(n)).

%t Array[PrimeNu@ If[# == 1, 1, GCD @@ {Block[{k = #, m = 0}, Times @@ Power @@@ Table[k -= m; k = DeleteCases[k, 0]; {Prime@ Length@ k, m = Min@ k}, Length@ Union@ k]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ #], Function[t, Times @@ Prime@ Accumulate[If[Length@ t < 2, {0}, Join[{1}, ConstantArray[0, Length@ t - 2], {-1}]] + ReplacePart[t, Map[#1 -> #2 & @@ # &, #]]]]@ ConstantArray[0, Transpose[#][[1, -1]]] &[# /. {p_, e_} /; p > 0 :> {PrimePi@ p, e}]} &@ FactorInteger[#]] &, 105] (* _Michael De Vlieger_, Jan 24 2020, after _JungHwan Min_ at A122111. *)

%o (PARI) A331596(n) = omega(gcd(A122111(n), A241909(n)));

%Y Cf. A001221, A331596, A331597.

%K nonn

%O 1,15

%A _Antti Karttunen_, Jan 22 2020