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%I #21 Mar 13 2014 00:57:43
%S 5,55,1430,4862,1463,1193010,1015,9414328,18278,749398,370577311,
%T 16723070,225398683020,7151980,378683037040,149846840,8511300512,
%U 272994644359580,194480021970,8516063242041795,8175951659117794,50,42925,3046258475,391139588190,1242164,1646644081775,2271776,38642514470976,4683175503770976
%N a(n) = binomial(prime(n),s)/prime(n) where s is the sum of the decimal digits of prime(n).
%C Note that a(n) is always an integer, as binomial(p,s) = p! / ((p-s)!/s!) is always divisible by p for prime p because neither (p-s)! nor s! can contain a factor of p when 0 < s < p, which occurs when n >= 5. By contrast, for n < 5, p(n) < 10, the sum of digits is p(n) itself, and the result is 1/p(n).
%e For n = 6, prime(6) = 13, s = 1+3 = 4 and binomial(13, 4)/13 = 715/13 = 55.
%p A007605 := proc(n) A007953(ithprime(n)) ; end proc:
%p A176267 := proc(n) local p; p := ithprime(n) ; binomial(p,A007605(n))/p ; end proc:
%p seq(A176267(n),n=5..20) ;
%t pn[n_]:=Module[{pr=Prime[n]},Binomial[pr,Total[IntegerDigits[pr]]]/pr]; Array[pn,40,5] (* _Harvey P. Dale_, Mar 29 2012 *)
%o (Sage) A176267 = lambda n: binomial(nth_prime(n), sum(nth_prime(n).digits()))/nth_prime(n) # _D. S. McNeil_, Dec 08 2010
%Y Cf. A176266, A007605.
%K nonn,base
%O 5,1
%A _Michel Lagneau_, Dec 07 2010
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