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 A076109 Least positive k such that k^n is the sum of n consecutive integers, or 0 if no such k exists. 4
 1, 1, 3, 0, 5, 3, 7, 0, 3, 5, 11, 0, 13, 7, 15, 0, 17, 3, 19, 0, 21, 11, 23, 0, 5, 13, 3, 0, 29, 15, 31, 0, 33, 17, 35, 0, 37, 19, 39, 0, 41, 21, 43, 0, 15, 23, 47, 0, 7, 5, 51, 0, 53, 3, 55, 0, 57, 29, 59, 0, 61, 31, 21, 0, 65, 33, 67, 0, 69, 35, 71, 0, 73, 37, 15, 0, 77, 39, 79, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS No k exists precisely when n == 0 (mod 4). a(p) = p if p is a prime. LINKS FORMULA a(n) = (n*A076107(n)+(n^2-n)/2)^(1/n) for n != 0 (mod 4). a(n) = A076108^(1/n). Multiplicative with a(2^1) = 1; a(2^e) = 0 if e >= 2; a(p^e) = p if p >= 3. - David W. Wilson, Jun 10 2005 a(n) = A007947(n) if n == 1 (mod 2); A007947(n/2) if n == 2 (mod 4); 0 if n == 0 (mod 4). - David W. Wilson, Jun 10 2005 a(4k)=0; otherwise a(n)=p1*...*pm where p1, ..., pm are all distinct odd primes dividing n. - Max Alekseyev, Jun 10 2005 PROG (PARI) for(n=1, 100, t=n*(n-1)/2:f=0:for(r=1, 10^4, if((r^n-t)%n==0, f=r:break)):print1(f", ")) (PARI) {A076109(n)=if(n%4==0, return(0)); if(n%2==0, n\=2); f=factorint(n)[, 1]; prod(i=1, length(f), f[i])} (Alekseyev) CROSSREFS Cf. A076107, A076108. Sequence in context: A322937 A326989 A326937 * A078788 A284599 A005069 Adjacent sequences:  A076106 A076107 A076108 * A076110 A076111 A076112 KEYWORD nonn,mult AUTHOR Amarnath Murthy, Oct 08 2002 EXTENSIONS Corrected and extended by Ralf Stephan, Mar 30 2003 More terms from Max Alekseyev, Jun 10 2005 STATUS approved

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Last modified August 10 12:19 EDT 2020. Contains 336379 sequences. (Running on oeis4.)