OFFSET
1,2
COMMENTS
Equals left border of triangle A158951. - Gary W. Adamson, Mar 31 2009
Equals row sums of triangle A168509. - Gary W. Adamson, Nov 27 2009
Let c(d_x(n)) = (d_x(n) + 1) / 2 if d_x(n) == 1 (mod 2), and d_x(n) / 2 if d_x(n) == 0 (mod 2), where d_x(n) is the x-th divisor of n, 1 <= d_x(n) <= n, and c(d_x(n)) denotes the cardinality of said divisor within the ordered set of naturals sharing its parity. Then, a(n) = Sum_{i=1..A000005(n)} c(d_i(n)). - Christopher Hohl, Apr 16 2019
FORMULA
Inverse Moebius transform of A008619 (offset 1). - Michael Somos, Jun 11 2003
G.f.: Sum_{k>=1} x^k / ((1 - x^k) * (1 - x^(2*k))). - Michael Somos, Jun 11 2003
G.f.: Sum_{n>=1} A110654(n)*x^n/(1-x^n). - Mircea Merca, Feb 26 2014
EXAMPLE
There are 7 pairs (p,q), 0 <= p < q, such that p+q divides 6: (0,1), (0,2), (0,3), (0,6), (1, 2), (1, 5), (2, 4); thus a(6) = 7.
G.f. = x + 2*x^2 + 3*x^3 + 4*x^4 + 4*x^5 + 7*x^6 + 5*x^7 + 8*x^8 + 8*x^9 + ...
MAPLE
with(numtheory): seq((sigma(n)+tau(2*n)-tau(n))/2, n=1 .. 80); # - Ridouane Oudra, Sep 06 2020
PROG
(PARI) {a(n) = if( n<1, 0, sumdiv( n, d, (1 + d)\2))} /* Michael Somos, Jun 11 2003 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 03 2003
STATUS
approved