cp's OEIS Frontend

A238692 a(n) is the quotient of the sum of (not necessarily distinct) integers i!+(prime(n)-1)!/i!, i=1,2,...,prime(n)-2, which are divisible by prime(n), and prime(n).

%I A238692 #14 Jan 29 2023 19:30:06
%S A238692 0,1,7,139,365641,39916801,1317933016441,355688356705921,
%T A238692 53128667010491295649,10888872347627347035630931201,
%U A238692 8841761993746245283777145088001,10333147966386144929666651337523200000001
%N A238692 a(n) is the quotient of the sum of (not necessarily distinct) integers i!+(prime(n)-1)!/i!, i=1,2,...,prime(n)-2, which are divisible by prime(n), and prime(n).
%C A238692 a(n) is prime for n = {3,4,5,6,7,31,738}; a(738) ~ 7.1 * 10^18518. There are no others for n up to 1000. - _Peter J. C. Moses_, Mar 03 2014
%e A238692 Let n=4, prime(n)=7. Consider integers i!+6!/i!, i=1,2,3,4,5: 721,362,126,54,126. Among them 721,126,126 are divisible by 7. So a(4)=(721 + 126 + 126)/7 = 139.
%t A238692 Map[Total[Cases[Table[i!+(#-1)!/i!,{i,#-2}]/#,_Integer]]&,Prime[Range[10]]] (* _Peter J. C. Moses_, Mar 10 2014 *)
%Y A238692 Cf. A238444, A007619.
%K A238692 nonn
%O A238692 1,3
%A A238692 _Vladimir Shevelev_ and _Peter J. C. Moses_, Mar 03 2014