A368694 -id:A368694 - cp's OEIS frontend

A368695 Lexicographically earliest infinite sequence such that a(i) = a(j) => A368694(i) = A368694(j) for all i, j >= 0.

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

Offset: 0

Antti Karttunen, Jan 03 2024

Restricted growth sequence transform of A368694, where A368694 is the Dirichlet inverse of the highest power of two that divides sigma(n), applied to A163511(n).

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A163511, A082903, A366889, A368694.

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; };
A082903(n) = (2^valuation(sigma(n), 2));
memoA366889 = Map();
A366889(n) = if(1==n,1,my(v); if(mapisdefined(memoA366889,n,&v), v, v = -sumdiv(n,d,if(dA082903(n/d)*A366889(d),0)); mapput(memoA366889,n,v); (v)));
A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A368694(n) = A366889(A163511(n));
v368695 = rgs_transform(vector(1+up_to,n,A368694(n-1)));
A368695(n) = v368695[1+n];

cp's OEIS Frontend

A368695 Lexicographically earliest infinite sequence such that a(i) = a(j) => A368694(i) = A368694(j) for all i, j >= 0.

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