|
|
A076108
|
|
Least positive n-th power that is the sum of n consecutive integers, or 0 if no such n-th power exists.
|
|
3
|
|
|
1, 1, 27, 0, 3125, 729, 823543, 0, 19683, 9765625, 285311670611, 0, 302875106592253, 678223072849, 437893890380859375, 0, 827240261886336764177, 387420489, 1978419655660313589123979, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
No n-th power exists precisely when n == 0 (mod 4).
The first term of the sum is A076107(n) for n != 0 (mod 4).
a(p) = p^p for prime p.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n*A076107(n)+(n^2-n)/2 for n != 0 (mod 4).
a(4k)=0; otherwise a(n)=p1^n*...*pm^n where p1, ..., pm are all distinct odd primes dividing n. - Max Alekseyev, Jun 10 2005
|
|
EXAMPLE
|
27 = 3^3 = 8+9+10 is least positive cube that is sum of 3 consecutive integers, hence a(3) = 27.
|
|
PROG
|
(PARI) for(n=1, 30, t=n*(n-1)/2:f=0:for(r=1, 10^4, if((r^n-t)%n==0, f=r^n:break)):print1(f", "))
(PARI) {A076108(n)=if(n%4==0, return(0)); m=n; if(m%2==0, m\=2); f=factorint(m)[, 1]; prod(i=1, length(f), f[i])^n} (Alekseyev)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|