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A238692 a(n) is the quotient of sum of (not necessary distinct) integers i!+(prime(n)-1)!/i!, i=1,2,...,prime(n)-2, which are divisible by prime(n), and prime(n). 1
0, 1, 7, 139, 365641, 39916801, 1317933016441, 355688356705921, 53128667010491295649, 10888872347627347035630931201, 8841761993746245283777145088001, 10333147966386144929666651337523200000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Cf. A238444, A007619.

Sequence in context: A126156 A082162 A280629 * A288322 A297650 A085708

Adjacent sequences:  A238689 A238690 A238691 * A238693 A238694 A238695

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 14 19:47 EDT 2020. Contains 336483 sequences. (Running on oeis4.)