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 A303762 #33 Jun 07 2018 22:10:11
%S A303762 1,2,6,3,15,5,10,30,210,105,35,7,14,42,21,231,77,11,22,66,33,165,55,
%T A303762 110,330,2310,1155,385,770,154,462,6006,3003,1001,143,13,26,78,39,195,
%U A303762 65,130,390,2730,1365,455,91,182,546,273,4641,1547,221,17,34,102,51,255,85,170,510,3570,1785,595,119,238,714,357,3927,1309,187,374,1122,561,2805,935
%N A303762 a(0) = 1, and for n >= 1, a(n) is either the largest divisor of a(n-1) not already present in the sequence, or (if all divisors already used), a(n-1) * {the least prime p such that p does not divide a(n-1) and p*a(n-1) is not already present}.
%C A303762 Each a(n+1) is either a divisor or a multiple of a(n).
%C A303762 The construction is otherwise like that of A303760, except here we choose the largest divisor instead of the smallest one. In contrast to A303760, this sequence is NOT permutation of A005117: 70 = A019565(13) is the first missing squarefree number. See also comments in A303769, A303749 and A302775.
%C A303762 Index of greatest prime factor of a(n) is monotonic and increments at n = {0, 1, 2, 4, 8, 15, 31, 50, 102, 157, 317, 480, 964, 1451, 2907, 4366, 8738, 13113, 26233, 39356, ...} - _Michael De Vlieger_, May 22 2018
%H A303762 Antti Karttunen, <a href="/A303762/b303762.txt">Table of n, a(n) for n = 0..26232</a>
%F A303762 a(n) = A019565(A303769(n)). [Conjectured]
%e A303762 From _Michael De Vlieger_, May 23 2018: (Start)
%e A303762 Table below shows the initial 31 terms at right. First column is index n. Second shows "." if a(n) = largest divisor of a(n-1), or factor p. Third shows presence "1" or absence "." of prime k among prime divisors of a(n).
%e A303762 n p\d MN(n) a(n)
%e A303762 ---------------------------
%e A303762 0 . . 1
%e A303762 1 2 1 2
%e A303762 2 3 11 6
%e A303762 3 . .1 3
%e A303762 4 5 .11 15
%e A303762 5 . ..1 5
%e A303762 6 2 1.1 10
%e A303762 7 3 111 30
%e A303762 8 7 1111 210
%e A303762 9 . .111 105
%e A303762 10 . ..11 35
%e A303762 11 . ...1 7
%e A303762 12 2 1..1 14
%e A303762 13 3 11.1 42
%e A303762 14 . .1.1 21
%e A303762 15 11 .1.11 231
%e A303762 16 . ...11 77
%e A303762 17 . ....1 11
%e A303762 18 2 1...1 22
%e A303762 19 3 11..1 66
%e A303762 20 . .1..1 33
%e A303762 21 5 .11.1 165
%e A303762 22 . ..1.1 55
%e A303762 23 2 1.1.1 110
%e A303762 24 3 111.1 330
%e A303762 25 7 11111 2310
%e A303762 26 . .1111 1155
%e A303762 27 . ..111 385
%e A303762 28 2 1.111 770
%e A303762 29 . 1..11 154
%e A303762 30 3 11.11 462
%e A303762 31 13 11.111 6006
%e A303762 ... (End)
%t A303762 Nest[Append[#, Block[{d = Divisors@ #[[-1]], p = 2}, If[Complement[d, #] != {}, Complement[d, #][[-1]], While[Nand[Mod[#[[-1]], p] != 0, FreeQ[#, p #[[-1]] ] ], p = NextPrime@ p]; p #[[-1]] ] ] ] &, {1}, 75] (* _Michael De Vlieger_, May 22 2018 *)
%o A303762 (PARI)
%o A303762 default(parisizemax,2^31);
%o A303762 up_to = 2^14;
%o A303762 A053669(n) = forprime(p=2, , if (n % p, return(p))); \\ From A053669
%o A303762 v303762 = vector(up_to);
%o A303762 m_inverses = Map();
%o A303762 prev=1; for(n=1,up_to,fordiv(prev,d,if(!mapisdefined(m_inverses,(prev/d)),v303762[n] = (prev/d);mapput(m_inverses,(prev/d),n);break)); if(!v303762[n], apu = prev; while(mapisdefined(m_inverses,try = prev*A053669(apu)), apu *= A053669(apu)); v303762[n] = try; mapput(m_inverses,try,n)); prev = v303762[n]);
%o A303762 A303762(n) = v303762[n+1];
%Y A303762 Subset of A005117.
%Y A303762 Cf. also A019565, A302774, A302775, A303749, A303769.
%Y A303762 Cf. A303760, A303761 (variants).
%K A303762 nonn
%O A303762 0,2
%A A303762 _Antti Karttunen_, May 03 2018