This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A304978 #50 Jun 20 2025 01:29:44
%S A304978 106,155,197,204,253,288,302,351,379,400,421,449,470,498,504,535,547,
%T A304978 554,561,596,645,652,687,694,704,729,743,779,782,792,820,834,841,873,
%U A304978 890,904,925,939,953,988,1016,1029,1037,1042,1054,1079,1086,1107,1121,1135,1184,1198,1204,1211,1219,1233,1254,1276,1282,1289,1329
%N A304978 Numbers that can be expressed in more than one way as 6xy + x + y with x >= y > 0.
%C A304978 Is it possible to find a closed form formula for this sequence?
%C A304978 Numbers k such that 6*k+1 has at least 5 divisors == 1 (mod 6). - _Robert Israel_, Jan 20 2019
%H A304978 Robert Israel, <a href="/A304978/b304978.txt">Table of n, a(n) for n = 1..10000</a>
%e A304978 106 is in this sequence because 106 can be expressed in two different ways as 6xy + x + y: 6*8*2 + 8 + 2 and 6*15*1 + 15 + 1.
%p A304978 filter:= proc(n) nops(select(t -> t mod 6 =1, numtheory:-divisors(6*n+1)))>= 5 end proc:
%p A304978 select(filter, [$1..2000]); # _Robert Israel_, Jan 20 2019
%t A304978 Select[Range[1329], 2 == Length@ FindInstance[ 6*x*y+x+y == # && x >= y > 0, {x, y}, Integers, 2] &] (* _Giovanni Resta_, May 29 2018 *)
%o A304978 (Python)
%o A304978 from sympy import divisors
%o A304978 def ok(n): return sum(d%6 == 1 for d in divisors(6*n+1)) > 4
%o A304978 print([n for n in range(1330) if ok(n)]) # _David Radcliffe_, Jun 19 2025
%o A304978 (PARI) is(n) = my(i=0); for(x=1, n, for(y=1, x, if(n==6*x*y+x+y, i++; if(i==2, return(1))))); 0 \\ _Felix Fröhlich_, May 29 2018
%Y A304978 Subsequence of A067611. A279060.
%K A304978 nonn
%O A304978 1,1
%A A304978 _Pedro Caceres_, May 22 2018