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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Nov 29 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A014197(n), A081373(n)].

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A014197, A081373, A305896, A319339, A322023.

Programs

PARI

up_to = 65537;
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; };
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; };
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
v081373 = ordinal_transform(vector(up_to,n,eulerphi(n)));
A081373(n) = v081373[n];
v322024 = rgs_transform(vector(up_to, n, [A014197(n), A081373(n)]));
A322024(n) = v322024[n];