A336149 - OEIS

%I #7 Jul 13 2020 07:54:41

%S 1,2,3,2,4,5,6,2,7,8,9,5,10,11,12,2,13,14,15,8,16,17,18,5,19,20,21,11,

%T 22,23,24,2,25,26,27,14,28,29,30,8,31,32,33,17,34,35,36,5,37,38,39,20,

%U 40,41,42,11,43,44,45,23,46,47,48,2,49,50,51,26,52,53,54,14,55,56,34,29,57,58,59,8,60,61,62,32,63,64,65,17,66,67,68,35,69,70,71,5,72,27,73,38,74,75,76,20,77

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A278222(i) = A278222(j), for all i, j >= 1.

%C Restricted growth sequence transform of the ordered pair [A278221(n), A278222(n)], i.e., of the ordered pair [A046523(A122111(n)), A046523(A005940(1+n))].

%C For all i, j: A336146(i) = A336146(j) => a(i) = a(j) => A035531(i) = A035531(j).

%H Antti Karttunen, <a href="/A336149/b336149.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523

%o A278221(n) = A046523(A122111(n));

%o A278222(n) = A046523(A005940(1+n));

%o Aux336149(n) = [A278221(n),A278222(n)];

%o v336149 = rgs_transform(vector(up_to, n, Aux336149(n)));

%o A336149(n) = v336149[n];

%Y Cf. A005940, A046523, A064989, A122111, A278221, A278222.

%Y Cf. also A035531, A286621, A286622, A324400, A336146, A336148, A336159.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 12 2020