A369065 -id:A369065 - cp's OEIS frontend

A369459 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369458(i) = A369458(j) for all i, j >= 0.

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

Offset: 0

Antti Karttunen, Jan 28 2024

nonn

Restricted growth sequence transform of A369458.
For all i, j >= 1:
  A003602(i) = A003602(j) => A369467(i) = A369467(j) => a(i) = a(j).

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

Cf. A000265, A003415, A003602, A163511, A369458, A369465, A369467.

Cf. also A369065.

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>>valuation(n,2));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
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));
A369458(n) = A003415(A000265(A163511(n)));
v369459 = rgs_transform(vector(1+up_to,n,A369458(n-1)));
A369459(n) = v369459[1+n];

For all n > 0, a(n) = a(2*n) = a(A000265(n)).

A369457 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369456(i) = A369456(j) for all i, j >= 0.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Jan 27 2024

nonn

Restricted growth sequence transform of A369456.

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

Cf. A005940, A083345, A369456.

Cf. also A366802, A369065, A369067.

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369456(n) = A083345(A005940(1+n));
v369457 = rgs_transform(vector(1+up_to,n,A369456(n-1)));
A369457(n) = v369457[1+n];

cp's OEIS Frontend

A369459 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369458(i) = A369458(j) for all i, j >= 0.

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