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.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A001414, A000254, A024451.

Sequence in context: A344047 A344060 A140362 * A269679 A211056 A269468

Adjacent sequences: A159835 A159836 A159837 * A159839 A159840 A159841

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