This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A320626 a(n) = (A006134(prime(n)-1) - Legendre(prime(n), 3))/prime(n)^2. 1
 1, 1, 4, 26, 2074, 21660, 2804068, 33847970, 5345496688, 12201269878660, 165029257057602, 433037204976615540, 85637003420093445994, 1215603499085916654728, 248871244937134915010626, 753881874165723132009014662, 2359161060012378685209851991166 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is always an integer. Are there any primes p such that p^3 divides A006134(p-1) - Legendre(p, 3)? LINKS EXAMPLE a(1) = (binomial(0, 0) + binomial(2, 1) + 1)/4 = 4/4 = 1. a(2) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2))/9 = 9/9 = 1. a(3) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + binomial(6, 3) + binomial(8, 4) + 1)/25 = 100/25 = 4. PROG (PARI) A006134(n) = sum(k=0, n, binomial(2*k, k)) a(n) = my(p=prime(n)); (A006134(p-1) - kronecker(p, 3))/p^2 CROSSREFS Cf. A006134, A102283, A320624. Sequence in context: A322395 A326264 A132488 * A144990 A102199 A125723 Adjacent sequences:  A320623 A320624 A320625 * A320627 A320628 A320629 KEYWORD nonn AUTHOR Jianing Song, Oct 18 2018 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 September 18 09:56 EDT 2019. Contains 327169 sequences. (Running on oeis4.)