|
| |
|
|
A127165
|
|
a(n) = the maximum prime S possible, if S = product of b(k)'s + product of c(k)'s, where the distinct positive integers <= n are partitioned into the two sets {b(k)} and {c(k)}. a(n) = 0 if no prime S exists for that n.
|
|
3
| |
|
|
2, 2, 3, 7, 11, 43, 149, 1013, 8069, 0, 0, 39916801, 43545611, 566092811, 7925299211, 118879488011, 1609445376013, 32335220736011, 44771844096143, 582033973248209, 221172909834240011, 3930072474746880013
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| a(0)=a(1)=2 because the product over the empty set is defined here as 1. For S to be a prime, the positive integers <= n, except 1 and the primes > n/2, must all be together in either {b(k)} or {c(k)}. If p is a prime where n/2 < p <= n, then it is possible that p is in either product of the S sum, as can 1. Terms calculated by Edwin Clark.
|
|
|
LINKS
| Ray Chandler, Table of n, a(n) for n=0..100
|
|
|
EXAMPLE
| For n = 6 we have the only prime S (and so the maximum prime S) with S = 1*2*3*4*6 + 5 = 149.
|
|
|
MATHEMATICA
| f[n_] := Block[{d = Divisors[Times @@ Select[Range[n], PrimeQ[ # ] && 2# > n &]]}, Select[Union[d + n!/d], PrimeQ]]; If[ # == {}, 0, Last[ # ]] & /@ Array[f, 30, 0] (*Chandler*)
|
|
|
CROSSREFS
| Cf. A127166, A128199.
Sequence in context: A065383 A087384 A179283 * A100683 A153940 A049905
Adjacent sequences: A127162 A127163 A127164 * A127166 A127167 A127168
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Leroy Quet Jan 06 2007
|
|
|
EXTENSIONS
| a(21)-a(35) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 2007
|
| |
|
|
