|
Search: id:A111775
|
|
|
| A111775 |
|
Number of ways n can be written as a sum of at least three consecutive integers. |
|
+0
3
|
|
| 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 2, 0, 1, 2, 1, 0, 1, 1, 1, 2, 1, 0, 3, 0, 0, 2, 1, 2, 2, 0, 1, 2, 1, 0, 3, 0, 1, 4, 1, 0, 1, 1, 2, 2, 1, 0, 3, 2, 1, 2, 1, 0, 3, 0, 1, 4, 0, 2, 3, 0, 1, 2, 3, 0, 2, 0, 1, 4, 1, 2, 3, 0, 1, 3, 1, 0, 3, 2, 1, 2, 1, 0, 5, 2, 1, 2, 1, 2, 1, 0, 2, 4, 2, 0, 3, 0, 1
(list; graph; listen)
|
|
|
OFFSET
|
1,16
|
|
|
COMMENT
|
Powers of 2 and (odd) primes can not be written as a sum of at least three consecutive integers. a(n) strongly depends on the number of odd divisors of n (A001227): Suppose n is to be written as sum of k consecutive integers starting with m, then 2n = k(2m + k - 1). Only one of the factors is odd. For each odd divisor of n there is a unique corresponding k, k=1 and k=2 must be excluded.
|
|
REFERENCES
|
Nieuw Archief voor Wiskunde 5/6 nr. 2 Problems/UWC Problem C part 4, Jun 2005, p. 181-182
|
|
LINKS
|
K. S. Brown's Mathpages, Partitions into Consecutive Integers
Nieuw Archief voor Wiskunde 5/6 nr. 2 Problems/UWC, Problem C: solution of this Problem
J. Spies, SAGE program for computing A111775
A. Heiligenbrunner, Sum of adjacent numbers (in German).
|
|
FORMULA
|
For n > 1: if n is even a(n)=A001227(n)-1=A069283(n) else a(n)=A001227(n)-2
|
|
EXAMPLE
|
a(15)=2 because 15 = 4+5+6 and 15 = 1+2+3+4+5. The number of odd divisors of 15 is 4.
|
|
MAPLE
|
A001227:= proc(n) local d, s; s := 0: for d from 1 by 2 to n do if n mod d = 0 then s:=s+1 fi: end do: return(s); end proc; A111775:= proc(n) local k; if n=1 then return(0) fi: k := A001227(n): if type(n, even) then k:=k-1 else k:=k-2 fi: return k; end proc; seq(A111775(i), i=1..150);
|
|
CROSSREFS
|
Cf. A111774, A001227 (number of odd divisors), A069283.
Sequence in context: A101670 A118683 A112605 this_sequence A025844 A035461 A029305
Adjacent sequences: A111772 A111773 A111774 this_sequence A111776 A111777 A111778
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jaap Spies (j.spies(AT)hccnet.nl), Aug 16 2005
|
|
|
Search completed in 0.002 seconds
|
