cp's OEIS Frontend

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

%I A076108 #11 Jan 28 2023 11:58:04
%S A076108 1,1,27,0,3125,729,823543,0,19683,9765625,285311670611,0,
%T A076108 302875106592253,678223072849,437893890380859375,0,
%U A076108 827240261886336764177,387420489,1978419655660313589123979,0
%N A076108 Least positive n-th power that is the sum of n consecutive integers, or 0 if no such n-th power exists.
%C A076108 No n-th power exists precisely when n == 0 (mod 4).
%C A076108 The first term of the sum is A076107(n) for n != 0 (mod 4).
%C A076108 a(p) = p^p for prime p.
%F A076108 a(n) = n*A076107(n)+(n^2-n)/2 for n != 0 (mod 4).
%F A076108 a(n) = A076109(n)^n.
%F A076108 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
%e A076108 27 = 3^3 = 8+9+10 is least positive cube that is sum of 3 consecutive integers, hence a(3) = 27.
%o A076108 (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","))
%o A076108 (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)
%Y A076108 Cf. A076107, A076109.
%K A076108 nonn
%O A076108 1,3
%A A076108 _Amarnath Murthy_, Oct 08 2002
%E A076108 Corrected and extended by _Ralf Stephan_, Mar 30 2003
%E A076108 Revised by _Max Alekseyev_ and _David W. Wilson_, Jun 10 2005
%E A076108 More terms from _Max Alekseyev_, Jun 10 2005