A275464 - OEIS

%I #20 Feb 23 2018 23:39:16

%S 0,0,0,3,1,1,6,2,2,9,3,10,12,5,5,15,15,7,18,8,8,21,9,21,24,11,25,27,

%T 13,13,30,30,15,33,16,16,36,35,18,39,19,40,42,21,42,45,45,24,48,25,25,

%U 51,26,26,54,27,55,57,56,56,60,60,33,63,34,63,66,36,36,69,67,70,72,40,40,75,75,42,78,77,44,81

%N a(n) = n - A038802(n).

%H Raphael Ranna, <a href="/A275464/b275464.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n - (A049084(A020639(2n+1)) - 1).

%F a(n) = n + O(n/log n). - _Charles R Greathouse IV_, Jul 29 2016

%e 9 = (2^0)*(3^2), resulting in 1 zero. So, a(4) = 4 - 1 = 3.

%t Table[f = FactorInteger[2 n + 1]; n - (PrimePi[f[[1, 1]]] - 1), {n, 100}]

%o (PARI) lpf(n)=factor(n)[1,1]

%o a(n)=n - primepi(lpf(2*n+1)) + 1 \\ _Charles R Greathouse IV_, Jul 29 2016

%Y Cf. A038802.

%K nonn

%O 1,4

%A _Raphael Ranna_, Jul 28 2016

%E Duplicate a(44)-a(45) removed by _Andrew Howroyd_, Feb 23 2018