cp's OEIS Frontend

A335420 a(n) = A000120(A163511(n)).

%I A335420 #15 Jul 25 2023 20:42:24
%S A335420 1,1,1,2,1,2,2,2,1,4,2,3,2,4,2,3,1,3,4,6,2,4,3,3,2,4,4,3,2,3,3,3,1,6,
%T A335420 3,5,4,7,6,6,2,4,4,6,3,4,3,5,2,4,4,6,4,4,3,4,2,6,3,5,3,2,3,3,1,6,6,6,
%U A335420 3,7,5,5,4,5,7,7,6,3,6,6,2,5,4,5,4,8,6,7,3,6,4,6,3,6,5,4,2,5,4,7,4,4,6,5,4,6
%N A335420 a(n) = A000120(A163511(n)).
%H A335420 Antti Karttunen, <a href="/A335420/b335420.txt">Table of n, a(n) for n = 0..65537</a>
%H A335420 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A335420 a(n) = A000120(A163511(n)).
%F A335420 a(n) = A001222(A335422(n)).
%F A335420 a(n) = a(2n) = a(A000265(n)).
%F A335420 For all n >= 0, a(2^n) = 1.
%o A335420 (PARI)
%o A335420 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A335420 A054429(n) = ((3<<#binary(n\2))-n-1);
%o A335420 A163511(n) = if(!n,1,A005940(1+A054429(n)));
%o A335420 A335420(n) = hammingweight(A163511(n));
%o A335420 (Python)
%o A335420 from sympy import nextprime
%o A335420 def A335420(n):
%o A335420     c, p, k = 1, 1, n
%o A335420     while k:
%o A335420         c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
%o A335420         k >>= s+1
%o A335420     return (c*p).bit_count() # _Chai Wah Wu_, Jul 25 2023
%Y A335420 Cf. A000079 (positions of ones), A000120, A001222, A163511, A335421, A335422.
%Y A335420 Cf. also A323901, A334204.
%K A335420 nonn
%O A335420 0,4
%A A335420 _Antti Karttunen_, Jun 09 2020