A329169 Numbers k such that k=(a+b)*c=a*b+c for more than one triple (a,b,c) with 1<c<a<=b.

3000, 4422, 22425, 25344, 35178, 44135, 49329, 81075, 128640, 143792, 154698, 182970, 291330, 341320, 389064, 413424, 451248, 581280, 593670, 638370, 662784, 686546, 714840, 807534, 891324, 905240, 906980, 934800, 1005039, 1072720, 1164672, 1326528, 1350174, 1369764, 1438080, 1478048, 1487525

Offset

1,1

Comments

The first term with more than two triples is 38601360, corresponding to (a,b,c) = (1794, 21516, 1656), (3180, 12138, 2520) and (6015, 6417, 3105).

Links

Robert Israel, Table of n, a(n) for n = 1..162

Example

a(3)=22425 is a member because we can take (a,b,c)=(149,150,75) or (42,533,39):
22425 = (149+150)*75 = 149*150+75 = (42+533)*39 = 42*533+39.

Maple

N:= 10^7: # 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:
S:= sort([Res]):
J:= select(i -> S[i+1]=S[i], [$1..nops(S)-1]):
sort(convert(convert(S[J], set), list));

Crossrefs

Subsequence of A191676.

Sequence in context: A119892 A333013 A158861 * A236982 A202097 A229782

Adjacent sequences: A329166 A329167 A329168 * A329170 A329171 A329172

Keyword

nonn

Author

Robert Israel, Nov 06 2019

Status

approved