A063749 - OEIS

A063749

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

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, 52, 0, 36, 20, 16, 24, 75, 0, 18, 24, 74, 0, 76, 0, 51, 60, 22, 0, 121, 18, 60, 32, 61, 0, 100, 40, 108, 36, 28, 0, 198, 0, 30, 88, 100, 48, 124, 0, 81, 44, 140, 0, 243, 0, 36, 104

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

COMMENTS

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

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

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

PROG

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