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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 (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(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

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Last modified September 25 19:14 EDT 2020. Contains 337344 sequences. (Running on oeis4.)