cp's OEIS Frontend

A322024 Lexicographically earliest such sequence a that a(i) = a(j) => A014197(i) = A014197(j) and A081373(i) = A081373(j), for all i, j. Here A081373(n) gives the number of k, 1 <= k <= n, with phi(k) = phi(n), while A014197(n) gives the number of integers m with phi(m) = n.

%I A322024 #6 Dec 02 2018 20:53:34
%S A322024 1,2,3,4,3,5,3,6,7,8,3,9,3,10,3,11,3,12,3,13,7,14,3,15,3,10,7,16,3,17,
%T A322024 3,18,7,10,3,19,3,10,7,20,3,21,3,22,10,14,3,23,7,24,3,16,3,16,7,25,7,
%U A322024 14,3,26,3,7,10,27,3,17,3,10,3,28,3,29,3,24,10,30,7,31,3,15,3,16,3,32,3,10,3,33,3,34,7,2,10,7,10,35,3,24,24,21,3,28,3,2,10
%N A322024 Lexicographically earliest such sequence a that a(i) = a(j) => A014197(i) = A014197(j) and A081373(i) = A081373(j), for all i, j. Here A081373(n) gives the number of k, 1 <= k <= n, with phi(k) = phi(n), while A014197(n) gives the number of integers m with phi(m) = n.
%C A322024 Restricted growth sequence transform of the ordered pair [A014197(n), A081373(n)].
%H A322024 Antti Karttunen, <a href="/A322024/b322024.txt">Table of n, a(n) for n = 1..65537</a>
%o A322024 (PARI)
%o A322024 up_to = 65537;
%o A322024 ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
%o A322024 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 A322024 A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))}; \\ From A014197
%o A322024 v081373 = ordinal_transform(vector(up_to,n,eulerphi(n)));
%o A322024 A081373(n) = v081373[n];
%o A322024 v322024 = rgs_transform(vector(up_to, n, [A014197(n), A081373(n)]));
%o A322024 A322024(n) = v322024[n];
%Y A322024 Cf. A014197, A081373, A305896, A319339, A322023.
%K A322024 nonn
%O A322024 1,2
%A A322024 _Antti Karttunen_, Nov 29 2018