A076108 Least positive n-th power that is the sum of n consecutive integers, or 0 if no such n-th power exists.

1, 1, 27, 0, 3125, 729, 823543, 0, 19683, 9765625, 285311670611, 0, 302875106592253, 678223072849, 437893890380859375, 0, 827240261886336764177, 387420489, 1978419655660313589123979, 0

Offset: 1

Author

Amarnath Murthy, Oct 08 2002

Keywords

• nonn

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.

Examples

			27 = 3^3 = 8+9+10 is least positive cube that is sum of 3 consecutive integers, hence a(3) = 27.
		

Crossrefs

Cf. A076107, A076109.

Programs

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)

Formula

a(n) = n*A076107(n)+(n^2-n)/2 for n != 0 (mod 4).

a(n) = A076109(n)^n.

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

Extensions

Corrected and extended by Ralf Stephan, Mar 30 2003

Revised by Max Alekseyev and David W. Wilson, Jun 10 2005

More terms from Max Alekseyev, Jun 10 2005