cp's OEIS Frontend

A305895 Filter sequence combining sum of proper divisors (A001065) and cototient (A051953) of n.

%I A305895 #6 Jun 14 2018 20:26:49
%S A305895 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A305895 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,
%U A305895 28,40,41,42,2,43,2,44,45,46,47,48,2,49,50,51,2,52,2,53,54,55,47,56,2,57,58,59,2,60,41,61,62,63,2,64,37,65,66,67,68,69,2,70,71,72,2,73,2,74,75
%N A305895 Filter sequence combining sum of proper divisors (A001065) and cototient (A051953) of n.
%C A305895 Restricted growth sequence transform of ordered pair [A001065(n), A051953(n)].
%H A305895 Antti Karttunen, <a href="/A305895/b305895.txt">Table of n, a(n) for n = 1..65537</a>
%F A305895 a(1) = 1; for n > 1, a(n) = 1 + A295885(n).
%o A305895 (PARI)
%o A305895 up_to = 65537;
%o A305895 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 A305895 A001065(n) = (sigma(n)-n);
%o A305895 A051953(n) = (n-eulerphi(n));
%o A305895 Aux305895(n) = [A001065(n), A051953(n)];
%o A305895 v305895 = rgs_transform(vector(up_to,n,Aux305895(n)));
%o A305895 A305895(n) = v305895[n];
%Y A305895 Cf. A001065, A051953, A295885, A305800.
%Y A305895 Differs from A300249 for the first time at n=105, where a(105) = 75, while A300249(105) = 56.
%Y A305895 Differs from A300235 for the first time at n=153, where a(153) = 110, while A300235(153) = 106.
%K A305895 nonn
%O A305895 1,2
%A A305895 _Antti Karttunen_, Jun 14 2018