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 A138180 #22 Nov 13 2016 12:36:09
%S A138180 1,1,2,3,8,1,2,3,4,5,8,9,15,24,80,1,2,3,4,5,6,7,8,9,14,15,20,24,27,35,
%T A138180 48,49,63,80,125,224,2400,4374,1,2,3,4,5,6,7,8,9,10,11,14,15,20,21,24,
%U A138180 27,32,35,44,48,49,54,55,63,80,98,99,120,125,175,224,242,384,440,539
%N A138180 Irregular triangle read by rows: row n consists of all numbers x such that x and x+1 have no prime factor larger than prime(n).
%C A138180 A number x is p-smooth if all prime factors of x are <= p. The length of row n is A002071(n). Row n begins with 1 and ends with A002072(n). Each term of row n-1 is in row n.
%C A138180 The n-th row is the union of the rows 1 to n of A145605. - _M. F. Hasler_, Jan 18 2015
%D A138180 See A002071.
%H A138180 T. D. Noe, <a href="/A138180/b138180.txt">Rows n=1..10 of triangle, flattened</a>
%e A138180 The table reads:
%e A138180 1,
%e A138180 1, 2, 3, 8,
%e A138180 1, 2, 3, 4, 5, 8, 9, 15, 24, 80, (= A085152)
%e A138180 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 20, 24, 27, 35, 48, 49, 63, 80, 125, 224, 2400, 4374, (= A085153)
%e A138180 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 20, 21, 24, 27, 32, 35, 44, 48, 49, 54, 55, 63, 80, 98, 99, 120, 125, 175, 224, 242, 384, 440, 539, 2400, 3024, 4374, 9800 (= A252494),
%e A138180 ...
%t A138180 (* This program needs x maxima taken from A002072. *) xMaxima = A002072; smoothNumbers[p_, max_] := Module[{a, aa, k, pp, iter}, k = PrimePi[p]; aa = Array[a, k]; pp = Prime[Range[k]]; iter = Table[{a[j], 0, PowerExpand @ Log[pp[[j]], max/Times @@ (Take[pp, j-1]^Take[aa, j-1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; row[n_] := Module[{sn}, sn = smoothNumbers[Prime[n], xMaxima[[n]]+1]; Reap[Do[If[sn[[i]]+1 == sn[[i+1]], Sow[sn[[i]]]], {i, 1, Length[sn]-1}]][[2, 1]]]; Table[Print[n]; row[n], {n, 1, 10}] // Flatten (* _Jean-François Alcover_, Jan 16 2015, updated Nov 10 2016 *)
%o A138180 (PARI) A138180_row=[]; A138180(n,k)={if(k, A138180(n)[k], #A138180_row<n && A138180_row=concat(A138180_row,vector(n)); if(#A138180_row[n], A138180_row[n], k=0; p=prime(n); A138180_row[n]=vector(A002071(n),i, until( vecmax(factor(k++)[, 1])<=p && vecmax(factor(k--+(k<2))[, 1])<=p,k++); k)))} \\ A138180(n) (w/o 2nd arg. k) returns the whole row. - _M. F. Hasler_, Jan 16 2015
%Y A138180 Cf. A145605; A085152, A085153, A252494, A252493, A252492.
%K A138180 nonn,tabf
%O A138180 1,3
%A A138180 _T. D. Noe_, Mar 04 2008