A191676 Numbers N such that N=(a+b)*c=a*b+c for some a,b,c>1.

14, 33, 39, 60, 64, 84, 95, 110, 138, 150, 155, 174, 189, 217, 248, 258, 259, 272, 315, 324, 360, 368, 390, 399, 405, 410, 430, 473, 504, 530, 539, 564, 584, 624, 663, 670, 732, 754, 770, 819, 852, 854, 869, 885, 897, 915, 1005, 1008, 1024, 1053, 1056, 1065, 1104, 1110, 1120, 1139, 1155, 1248, 1278, 1292, 1360, 1378, 1422

Offset

1,1

Comments

Without imposing c>1, there would be the trivial decomposition a=c=1, b=N-1, for any N.

One has a>c, b>c, since, e.g., a<=c would imply N = ab+c <= c(b+1) < c(b+a) = N. Therefore one can impose the restriction 1 < c < b <= a.

Links

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

Claudio Meller, posting on SeqFan mailing list, June 9, 2011.

Maple

N:= 10^4: # for terms <= N
Res:= NULL:
for a from 3 to N/3 do
   for b from 3 to a while a*b < N do
     c:= a*b/(a+b-1);
     if c::posint and c>1 then
       v:= (a+b)*c;
       if v<=N then Res:= Res, v fi
     fi
od od:
sort(convert({Res}, list)); # Robert Israel, Nov 06 2019

Mathematica

mx = 1424; lmt = Floor[9 Sqrt[mx]/2]; lst = {}; Do[ If[a*b + c == (a + b) c < mx, AppendTo[lst, a*b + c]], {a, 2, lmt}, {b, a + 1, lmt}, {c, 2, a - 1}]; Sort@ lst (* Robert G. Wilson v, Jun 17 2011 *)

Prog

(PARI) is_A191676(N)={fordiv(N, c, c*c>N & return; c>1 & fordiv(N-c, a, a*a>N-c & break; a>c & (a+(N-c)/a)*c==N & return(1)))}

Crossrefs

Sequence in context: A076329 A261560 A250186 * A191866 A162279 A367346

Adjacent sequences: A191673 A191674 A191675 * A191677 A191678 A191679

Keyword

nonn

Author

M. F. Hasler, based on suggestion of Claudio Meller (cf. link), Jun 10 2011

Status

approved