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).

0, 1, 7, 139, 365641, 39916801, 1317933016441, 355688356705921, 53128667010491295649, 10888872347627347035630931201, 8841761993746245283777145088001, 10333147966386144929666651337523200000001

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Mar 03 2014

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A238444, A007619.

Programs

Mathematica

Map[Total[Cases[Table[i!+(#-1)!/i!,{i,#-2}]/#,Integer]]&,Prime[Range[10]]] (* _Peter J. C. Moses, Mar 10 2014 *)