A072528 Table T(n,k) read by rows, giving number of occurrences of the remainder k when n is divided by i=1,2,3,...,n.
1, 2, 2, 1, 3, 1, 2, 2, 1, 4, 1, 1, 2, 3, 1, 1, 4, 1, 2, 1, 3, 3, 1, 1, 1, 4, 2, 2, 1, 1, 2, 3, 2, 2, 1, 1, 6, 1, 2, 1, 1, 1, 2, 5, 1, 2, 1, 1, 1, 4, 1, 4, 1, 2, 1, 1, 4, 3, 1, 3, 1, 1, 1, 1, 5, 3, 2, 1, 2, 1, 1, 1, 2, 4, 3, 2, 1, 2, 1, 1, 1, 6, 1, 3, 2, 2, 1, 1, 1, 1, 2, 5, 1, 3, 2, 2, 1, 1, 1, 1, 6, 1, 4, 1, 2
Offset: 1
Examples
The table begins 1 2 2 1 3 1 2 2 1 4 1 1 2 3 1 1 4 1 2 1
Formula
Let a(m) be the m-th term in the sequence. Then m=f(n)+k where f(1)=1 and f(n+1)=f(n)+floor((n+1)/2). n is the number being divided by the various i's and k is the remainder under consideration. f(n) has the generating function F(x)= (x(1+2x^2-2x^3))/((1-x)^2(1+x^2)) - Bruce Corrigan (scentman(AT)myfamily.com), Oct 22 2002
G.f. for k-th column: Sum_{m>0} x^((k+1)*m+k)/(1-x^m). - Vladeta Jovovic, Dec 16 2002
Extensions
Edited by Bruce Corrigan (scentman(AT)myfamily.com), Oct 22 2002
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 25 2003
Comments