login
a(n) = floor((A000005(n)*(n+1)/2) - A000203(n)).
1

%I #14 Jun 28 2018 04:49:20

%S 0,0,0,0,0,2,0,3,2,4,0,11,0,6,8,11,0,18,0,21,12,10,0,40,8,12,16,31,0,

%T 52,0,36,20,16,24,75,0,18,24,74,0,76,0,51,60,22,0,121,18,60,32,61,0,

%U 100,40,108,36,28,0,198,0,30,88,100,48,124,0,81,44,140,0,243,0,36,104

%N a(n) = floor((A000005(n)*(n+1)/2) - A000203(n)).

%C a(n) = 0 if n is prime, otherwise >= 0; first part of formula provides estimation of sigma(n).

%H Harry J. Smith, <a href="/A063749/b063749.txt">Table of n, a(n) for n = 1..1000</a>

%e n = 4: tau(4) = 3, (3*(4+1)/2) - 7 = 0.5 so a(4) = 0;

%e n = 12: tau(12) = 6, (6*(12+1)/2) - 28 = 39 - 28 = 11 = a(12).

%o (PARI) { for (n=1, 1000, a = numdiv(n)*(n + 1)\2 - sigma(n); write("b063749.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 29 2009

%Y Cf. A000005, A000203.

%K nonn

%O 1,6

%A _Labos Elemer_, Aug 14 2001