A365722 - OEIS

%I #16 Sep 17 2023 11:25:23

%S 0,1,1,1,2,2,2,3,2,1,2,2,2,3,3,3,4,3,2,3,3,3,4,4,4,5,3,1,2,2,2,3,3,3,

%T 4,3,2,3,3,3,4,4,4,5,4,3,4,4,4,5,5,5,6,4,2,3,3,3,4,4,4,5,4,3,4,4,4,5,

%U 5,5,6,5,4,5,5,5,6,6,6,7,4,1,2,2,2,3,3,3,4,3,2,3,3,3,4,4,4,5,4,3,4,4,4,5,5,5

%N The number of prime factors (with multiplicity) in A356867(1+n), where A356867 is Sycamore's Doudna variant D(3).

%C Sum of digits minus the number of trailing 2's in the base-3 representation of n (A007089).

%H Antti Karttunen, <a href="/A365722/b365722.txt">Table of n, a(n) for n = 0..59049</a>

%F a(n) = A001222(A356867(1+n)) = A001222(A365719(n)).

%F a(n) = A053735(n) - A007949(1+n).

%F a(n) >= A365721(n).

%o (PARI) A365722(n) = (sumdigits(n,3)-valuation(1+n,3));

%o (PARI) A365722(n) = bigomega(A356867(1+n)); \\ Uses also the program given in A356867.

%Y Cf. A001222, A007089, A007949, A053735, A356867, A365719, A365721.

%Y Cf. also A000120.

%K nonn,base

%O 0,5

%A _Antti Karttunen_, Sep 17 2023