A323914 Lexicographically earliest sequence such that a(i) = a(j) => A322994(i) = A322994(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 3, 6, 2, 5, 2, 7, 4, 8, 2, 9, 2, 8, 6, 10, 2, 8, 3, 11, 5, 12, 2, 13, 2, 12, 7, 14, 4, 8, 2, 15, 10, 12, 2, 16, 2, 17, 5, 18, 2, 12, 3, 19, 11, 20, 2, 21, 6, 17, 14, 22, 2, 8, 2, 23, 8, 17, 7, 24, 2, 25, 15, 26, 2, 12, 2, 27, 9, 28, 4, 29, 2, 17, 8, 30, 2, 12, 10, 31, 18, 20, 2, 21, 6, 32, 22, 33, 11, 17, 2, 34, 12, 12, 2, 35, 2, 25, 13

Offset: 1

Author

Antti Karttunen, Feb 12 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of A322994.

Links

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

Crossrefs

Cf. A156552, A297112, A322993, A322994.

Programs

PARI

up_to = 65537;
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; };
A000265(n) = (n/2^valuation(n, 2));
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)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A322993(n) = if(1==n,0,A000265(A156552(n)));
A322994(n) = sumdiv(n,d,moebius(n/d)*A322993(d));
v323914 = rgs_transform(vector(up_to,n,A322994(n)));
A323914(n) = v323914[n];