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

1,3

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

Table of n, a(n) for n=1..20.

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

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

Cf. A076107, A076109.

Sequence in context: A178737 A005067 A163574 * A040735 A040734 A040736

Adjacent sequences: A076105 A076106 A076107 * A076109 A076110 A076111

Keyword

nonn

Author

Amarnath Murthy, Oct 08 2002

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

Status

approved