A369459 -id:A369459 - cp's OEIS frontend

A369458 Arithmetic derivative of the odd part of n, permuted by A163511 ("Doudna-sequence mirrored").

0, 0, 0, 1, 0, 6, 1, 1, 0, 27, 6, 10, 1, 8, 1, 1, 0, 108, 27, 75, 6, 55, 10, 14, 1, 39, 8, 12, 1, 10, 1, 1, 0, 405, 108, 500, 27, 350, 75, 147, 6, 240, 55, 119, 10, 91, 14, 22, 1, 162, 39, 95, 8, 71, 12, 18, 1, 51, 10, 16, 1, 14, 1, 1, 0, 1458, 405, 3125, 108, 2125, 500, 1372, 27, 1425, 350, 1078, 75, 784, 147, 363

Offset: 0

Antti Karttunen, Jan 28 2024

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A000265, A003415, A163511, A369459 (rgs-transform), A369465.

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)));

a(n) = A369465(A163511(n)).

A369467 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369465(i) = A369465(j) and A369465(A163511(i)) = A369465(A163511(j)), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jan 28 2024

nonn

Restricted growth sequence transform of the ordered pair [A369458(n), A369465(n)], or equally, of the ordered pair [A369459(n), A369466(n)].

For all i, j >= 1: A003602(i) = A003602(j) => a(i) = a(j).

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

Cf. A000265, A003415, A003602, A163511, A349905, A369458, A369459, A369465, A369466.

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));
A369465(n) = A003415(A000265(n));
Aux369467(n) = [A369465(n), A369465(A163511(n))];
v369467 = rgs_transform(vector(up_to, n, Aux369467(n)));
A369467(n) = v369467[n];

cp's OEIS Frontend

A369458 Arithmetic derivative of the odd part of n, permuted by A163511 ("Doudna-sequence mirrored").

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