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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
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.
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
Sequence in context: A178737 A005067 A163574 * A040735 A040734 A040736
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