cp's OEIS Frontend

A293450 Restricted growth sequence transform of (3*A293225(n) + A010872(n)), a filter combining (n mod 3) with two products, the other formed from the 1-digits (A293221) and the other from the 2-digits (A293222) present in the ternary expansions of proper divisors of n.

%I A293450 #7 Nov 08 2017 22:32:33
%S A293450 1,2,3,4,2,5,6,7,8,9,2,10,6,11,12,13,2,14,6,15,16,17,2,18,19,20,21,22,
%T A293450 2,23,6,24,25,26,27,28,6,29,30,31,2,32,6,33,34,35,2,36,37,38,14,39,2,
%U A293450 40,41,42,43,44,2,45,6,46,47,48,49,50,6,51,52,53,2,54,6,55,56,57,58,59,6,60,61,62,2,63,64,65,66,67,2
%N A293450 Restricted growth sequence transform of (3*A293225(n) + A010872(n)), a filter combining (n mod 3) with two products, the other formed from the 1-digits (A293221) and the other from the 2-digits (A293222) present in the ternary expansions of proper divisors of n.
%H A293450 Antti Karttunen, <a href="/A293450/b293450.txt">Table of n, a(n) for n = 1..59049</a>
%F A293450 For all i, j: a(i) = a(j) => A002324(i) = A002324(j).
%o A293450 (PARI)
%o A293450 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 A293450 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A293450 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from _M. F. Hasler_
%o A293450 A289813(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==1, 1, 0)), 2); };
%o A293450 A289814(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
%o A293450 A293221(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A289813(d)))); m; };
%o A293450 A293222(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A289814(d)))); m; };
%o A293450 Anot_submitted(n) = (1/2)*(2 + ((A293222(n) + A293221(n))^2) - A293222(n) - 3*A293221(n)); \\ Eq.class-wise equal to A293225.
%o A293450 Anot2submitted(n) = ((3*Anot_submitted(n))+(n%3));
%o A293450 write_to_bfile(1,rgs_transform(vector(59049,n,Anot2submitted(n))),"b293450.txt");
%Y A293450 Cf. A002324, A010872, A293221, A293222, A293225, A293226.
%K A293450 nonn
%O A293450 1,2
%A A293450 _Antti Karttunen_, Nov 06 2017