This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A076107 First of n consecutive integers whose sum is a positive n-th power, or 0 if no such integers exist. 3
 1, 0, 8, 0, 623, 119, 117646, 0, 2183, 976558, 25937424596, 0, 23298085122475, 48444505197, 29192926025390618, 0, 48661191875666868473, 21523352, 104127350297911241532832, 0, 278218429446951548637196391 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS No sum exists precisely when n == 0 (mod 4). a(2) = 0 is a legitimate value. The sum is given by A076108(n) = A076109(n)^n for n != 0 (mod 4). a(p) = p^(p-1)-(p-1)/2 for prime p. LINKS FORMULA a(n) = A076108(n)/n-(n-1)/2 for n != 0 (mod 4). a(4k)=0; otherwise a(n) = (2*A076108(n)/n - n + 1)/2 = (2*p1^n*...*pm^n/n - n + 1)/2 where p1, ..., pm are all distinct odd primes dividing n. - Max Alekseyev, Jun 10 2005 EXAMPLE a(3) = 8 as 8+9+10 = 27 = 3^3. a(6) = 119 as 119+120+..+124 = 729 = 3^6. 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-t)/n:break)):print1(f", ")) (PARI) {A076107(n)=if(n%4==0, return(0)); m=n; if(m%2==0, m\=2); f=factorint(m)[, 1]; p=1; (2*prod(i=1, length(f), f[i])^n/n-n+1)/2} (Alekseyev) CROSSREFS Cf. A076108, A076109. Sequence in context: A221421 A013456 A180738 * A076952 A209914 A094922 Adjacent sequences:  A076104 A076105 A076106 * A076108 A076109 A076110 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 16 00:33 EST 2019. Contains 330013 sequences. (Running on oeis4.)