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 A291751 #72 Dec 19 2018 15:13:47
%S A291751 1,2,3,4,5,6,7,8,9,10,6,11,12,13,13,14,10,15,16,17,18,19,13,20,21,22,
%T A291751 23,24,25,26,18,27,28,29,28,30,31,32,33,34,22,35,36,37,38,26,28,39,40,
%U A291751 41,26,42,29,43,26,44,45,46,32,47,48,35,49,50,51,52,53,54,35,52,26,55,56,57,58,59,35,60,45,61,62,63,51,64,65,66,67,68,46,69,70,47,71
%N A291751 Lexicographically earliest such sequence a that a(i) = a(j) => A003557(i) = A003557(j) and A048250(i) = A048250(j), for all i, j.
%C A291751 Restricted growth sequence transform of A291750, which means that this is the lexicographically least sequence a, such that for all i, j: a(i) = a(j) <=> A291750(i) = A291750(j) <=> A003557(i) = A003557(j) and A048250(i) = A048250(j). That this is equal to the definition given in the title follows because any such lexicographically least sequence satisfying relation <=> is also the least sequence satisfying relation => with the same parameters.
%C A291751 Sigma (A000203) and psi (A001615) are functions of this sequence. See comments in A291750 for the reason. For example, to find the value of A001615(n) when we know just a(n), but without knowing n, let m be the least i for which a(i) = a(n); then A001615(n) = A003991(A291750(m)) = A003557(m) * A048250(m).
%H A291751 Antti Karttunen, <a href="/A291751/b291751.txt">Table of n, a(n) for n = 1..65537</a>
%o A291751 (PARI)
%o A291751 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A291751 A003557(n) = n/factorback(factor(n)[, 1]); \\ From A003557
%o A291751 A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
%o A291751 A291750(n) = (1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n));
%o A291751 v291751 = rgs_transform(vector(65537,n,A291750(n)));
%o A291751 A291751(n) = v291751[n];
%Y A291751 Cf. A001615, A003557, A048250, A291750, A291752, A294877, A295300, A295886, A295887, A295888, A319698, A322021.
%Y A291751 Differs from A286603 for the first time at n = 25, where a(25) = 21, while A286603(25) = 14.
%K A291751 nonn
%O A291751 1,2
%A A291751 _Antti Karttunen_, Sep 06 2017
%E A291751 Name changed and comments added by _Antti Karttunen_, Nov 24 2018