A082378 Positive integers that can be written in exactly one way as the product ab of positive integers where a+b is composite.

3, 4, 5, 7, 11, 12, 13, 17, 18, 19, 23, 28, 29, 31, 34, 37, 41, 43, 46, 47, 52, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 106, 107, 109, 113, 118, 127, 131, 137, 138, 139, 142, 148, 149, 151, 157, 163, 166, 167, 172, 173, 178, 179, 181, 191, 193, 197, 199

Offset

1,1

Comments

n is in the sequence if either: 1) n is an odd prime 2) n = 2 p where p is an odd prime and exactly one of 1+2p and 2+p is prime 3) n = 4 p where p is an odd prime and both 2p+1 and 2+p are prime

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

12 is included because of 1+12, 2+6, 3+4, only 2+6 is composite;
16 is not because 2+8 and 4+4 are both composite.

Maple

S:= NULL: for n from 1 to maxN do ct:= 0; for d in numtheory[divisors](n) do if d^2 > n then next fi; if not isprime(d+n/d) then ct:= ct+1; if ct > 1 then break fi fi; od; if ct = 1 then S:= S, n fi; od: S;

Mathematica

M = 200; Reap[For[n = 1, n <= M, n++, ct = 0; Do[If[d^2 > n, Continue[]]; If[CompositeQ[d + n/d], ct++; If[ct > 1, Break[]]], {d, Divisors[n]}]; If[ct == 1, Sow[n]]]][[2, 1]] (* Jean-François Alcover, Apr 29 2019, from Maple *)

Crossrefs

Sequence in context: A091428 A047499 A330109 * A046642 A330110 A330123

Adjacent sequences: A082375 A082376 A082377 * A082379 A082380 A082381

Keyword

easy,nonn

Author

Robert Israel, Sep 03 2004

Extensions

Offset changed by Robert Israel, Feb 26 2019

Status

approved