OFFSET
1,4
COMMENTS
Inverse Mobius transform of A004526. - R. J. Mathar, Jan 19 2009
FORMULA
G.f.: Sum_{n>=1} floor(n/2)*x^n/(1-x^n). - Joerg Arndt, Jan 30 2011
G.f.: Sum_{k>=1} x^(2*k) / ((1 + x^k) * (1 - x^k)^2). - Ilya Gutkovskiy, Aug 02 2021
a(n) = Sum_{i=1..floor(n/2)} A135539(n,2*i). - Ridouane Oudra, Apr 15 2022
EXAMPLE
10 has divisors 1,2,5,10. floor(d/2) gives 0,1,2,5, therefore a(10)=8.
MATHEMATICA
Table[Total[Floor[Divisors[n]/2]], {n, 80}] (* Harvey P. Dale, Feb 13 2023 *)
PROG
(PARI) for (n=1, 100, s=0; fordiv(i=n, i, s+=floor(i/2)); print1(", "s))
(PARI) a(n) = my(f = factor(n)); (sigma(f) - (numdiv(f)/(valuation(n, 2)+1)))>>1 \\ David A. Corneth, Apr 15 2022 using Franklin T. Adams-Watters's formula
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Perry, Jul 27 2003
STATUS
approved