A305976 - OEIS

%I #6 Jul 02 2018 20:25:12

%S 1,2,2,2,2,3,2,2,2,4,2,5,2,6,7,2,2,8,2,9,10,11,2,12,2,13,2,14,2,15,2,

%T 2,16,17,18,19,2,20,21,22,2,23,2,24,25,26,2,27,2,28,29,30,2,31,32,33,

%U 34,35,2,36,2,37,38,2,39,40,2,41,42,43,2,44,2,45,46,47,48,49,2,50,2,51,2,52,53,54,55,56,2,57,58,59,60,61,62,63,2,64,65,66,2

%N Filter sequence for a(prime^k) = constant sequences.

%H Antti Karttunen, <a href="/A305976/b305976.txt">Table of n, a(n) for n = 1..100000</a>

%F a(1) = 1, for n > 1, if A010055(n) = 1 [when n is in A246655], a(n) = 2, otherwise a(n) = 2+A085970(n) = running count from 3 onward.

%o (PARI)

%o up_to = 100000;

%o partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }

%o v065515 = partialsums(n -> (omega(n)<=1), up_to);

%o A065515(n) = v065515[n];

%o A085970(n) = (n - A065515(n));

%o A305976(n) = if(1==n,n,if(isprimepower(n),2,2+A085970(n)));

%Y Cf. A000961 (A246655), A085970, A305800, A305975, A305979.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 02 2018