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

1,2

Comments

The n-th row adds to n.

Links

Table of n, a(n) for n=1..105.

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

Example

The table begins
1
2
2 1
3 1
2 2 1
4 1 1
2 3 1 1
4 1 2 1

Crossrefs

Cf. A023645 for T(n, 2) and A072527 for T(n, 3).

Cf. A230374, A230399.

Sequence in context: A279287 A135352 A320040 * A368060 A227083 A327571

Adjacent sequences: A072525 A072526 A072527 * A072529 A072530 A072531

Keyword

nonn,tabl

Author

Amarnath Murthy, Aug 01 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

Status

approved