A339970 - OEIS

%I #8 Dec 27 2020 19:31:31

%S 0,1,1,2,2,3,3,4,2,3,3,4,4,5,5,6,2,3,3,4,4,5,5,6,4,5,5,6,6,7,7,8,1,2,

%T 2,3,3,4,4,5,3,4,4,5,5,6,6,7,3,4,4,5,5,6,6,7,5,6,6,7,7,8,8,9,3,4,4,5,

%U 5,6,6,7,5,6,6,7,7,8,8,9,5,6,6,7,7,8,8,9,7,8,8,9,9,10,10,11,4,5,5,6,6,7,7,8,6,7

%N a(n) = A329697(A019565(2n)).

%H Antti Karttunen, <a href="/A339970/b339970.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = A329697(A019565(2*n)) = A329697(A003961(A019565(n))).

%F a(n) = A329697(A339971(n)) + A000120(n).

%F If 4n = 2^e1 + 2^e2 + ... + 2^ek [e1 ... ek distinct], then a(n) = A329697(A000040(e1)) + A329697(A000040(e2)) + ... + A329697(A000040(ek)).

%o (PARI)

%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

%o A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));

%o A339970(n) = A329697(A019565(2*n));

%o (PARI) A339970(n) = { my(s=0, p=2); while(n>0, p = nextprime(1+p); if(n%2, s += A329697(p)); n >>= 1); (s); };

%Y Cf. A000040, A000120, A003961, A019565, A329697, A339971.

%Y Differs from A106486 for the first time at n=32, where a(32) = 1, while A106486(32) = 2.

%K nonn

%O 0,4

%A _Antti Karttunen_, Dec 27 2020