A323245 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A323244(n) for n > 1, and f(1) = -1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 3, 5, 2, 10, 2, 11, 12, 11, 2, 13, 14, 15, 4, 13, 2, 8, 2, 16, 17, 18, 19, 17, 2, 20, 21, 13, 2, 22, 2, 23, 24, 25, 2, 15, 21, 26, 24, 27, 2, 28, 29, 30, 21, 31, 2, 32, 2, 33, 9, 13, 8, 32, 2, 34, 35, 36, 2, 37, 2, 38, 8, 39, 40, 41, 2, 42, 21, 43, 2, 44, 45, 46, 47, 16, 2, 10, 48, 49, 50, 51, 52, 30, 2, 53, 14, 16, 2

Offset: 1

Author

Antti Karttunen, Jan 10 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of function f, defined as f(1) = -1, and for n > 1, f(n) = A033879(A156552(n)).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096

Programs

PARI

up_to = 1024;
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; };
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))));
A323244(n) = if(1==n, 0, my(k=A156552(n)); (2*k)-sigma(k));
A323245aux(n) = if(1==n,-1,A323244(n));
v323245 = rgs_transform(vector(up_to, n, A323245aux(n)));
A323245(n) = v323245[n];