login
A159838
Numbers n such that n*s and n-n*s are prime, where s is the sum of the reciprocals of the prime factors of n with repetition.
1
10, 66, 70, 78, 114, 130, 154, 174, 222, 238, 282, 310, 318, 370, 390, 418, 474, 510, 574, 618, 642, 670, 678, 690, 742, 754, 790, 798, 814, 822, 870, 874, 930, 978, 1090, 1122, 1162, 1182, 1218, 1230, 1374, 1378, 1398, 1434, 1498, 1542, 1554, 1570, 1578
OFFSET
1,1
COMMENTS
For n to qualify, the sum of these reciprocals must be less than one. For example, 350 = 2*5*5*7, with sum of reciprocals 1/2 + 1/5 + 1/5 + 1/7 = 73/70, which is greater than 1, so 350 is not in the sequence.
LINKS
EXAMPLE
Take 238 = 2*7*17 with sum of reciprocals 1/2 + 1/7 + 1/17 = 167/238, giving 238*(167/238) = 167 and 238-167=71. Both 167 and 71 are prime.
MATHEMATICA
srpfQ[n_]:=Module[{s=Total[Flatten[1/Table[First[#], {Last[#]}]&/@ FactorInteger[ n]]], ns}, ns=n*s; And@@PrimeQ[{ns, n-ns}]]; Select[Range[ 1600], srpfQ] (* Harvey P. Dale, Jul 01 2012 *)
PROG
(Magma) T:=[ Integers()!(n*&+[ d[2]/d[1]: d in Factorization(n) ]): n in [2..1600] ]; [ k+1: k in [1..#T] | IsPrime(s) and IsPrime((k+1-s)) where s is T[k] ]; // Klaus Brockhaus, Apr 27 2009
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
J. M. Bergot, Apr 23 2009
EXTENSIONS
Edited, 282 and 390 inserted, and extended beyond 418 by Klaus Brockhaus, Apr 27 2009
STATUS
approved