A176358 Partial sums of A002503.

5, 19, 46, 87, 131, 196, 272, 362, 471, 596, 735, 887, 1042, 1211, 1397, 1586, 1789, 1997, 2206, 2425, 2652, 2882, 3119, 3384, 3659, 3957, 4264, 4575, 4889, 5210, 5534, 5863, 6207, 6584, 6997, 7416, 7844, 8278, 8717, 9158, 9607, 10065, 10524, 10991

Offset

1,1

Comments

Partial sums of numbers n such that binomial(2n,n) is divisible by (n+1)^2. The subsequence of primes in this partial sum begins: 5, 19, 131, 887, 1789, 1997, 3119, 3659, 4889, 6997. The subsequence of primes in this partial sum begins: 196.

Links

Table of n, a(n) for n=1..44.

Formula

a(n) = SUM[i=1..n] A002503(i).

Example

a(23) = 5 + 14 + 27 + 41 + 44 + 65 + 76 + 90 + 109 + 125 + 139 + 152 + 155 + 169 + 186 + 189 + 203 + 208 + 209 + 219 + 227 + 230 + 237 = 3119 is prime.

Mathematica

Accumulate[Select[Range[800], Divisible[Binomial[2#, #], (#+1)^2]&]]  (* Harvey P. Dale, Apr 18 2011 *)

Crossrefs

Cf. A002503, A065350, A000108, A065344-A065349.

Sequence in context: A146395 A154302 A146736 * A045458 A120289 A243895

Adjacent sequences: A176355 A176356 A176357 * A176359 A176360 A176361

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 15 2010

Extensions

Corrected by Harvey P. Dale, Apr 18 2011.

Status

approved