A366798 -id:A366798 - cp's OEIS frontend

A366874 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366873(i) = A366873(j) for all i, j >= 0, where A366873 is the average of number of and sum of odd divisors of n as permuted by A163511.

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

Offset: 0

Antti Karttunen, Oct 27 2023

nonn

Restricted growth sequence transform of A366873.

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

Cf. A113415, A163511, A366873.

Cf. also A366798, A366806, A366878.

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; };
A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
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));
A366873(n) = A113415(A163511(n));
v366874 = rgs_transform(vector(1+up_to,n,A366873(n-1)));
A366874(n) = v366874[1+n];

A366797 Number of odd divisors permuted by A163511: a(n) = A001227(A163511(n)).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 4, 2, 2, 1, 5, 4, 4, 3, 6, 3, 3, 2, 6, 4, 4, 2, 4, 2, 2, 1, 6, 5, 5, 4, 8, 4, 4, 3, 9, 6, 6, 3, 6, 3, 3, 2, 8, 6, 6, 4, 8, 4, 4, 2, 6, 4, 4, 2, 4, 2, 2, 1, 7, 6, 6, 5, 10, 5, 5, 4, 12, 8, 8, 4, 8, 4, 4, 3, 12, 9, 9, 6, 12, 6, 6, 3, 9, 6, 6, 3, 6, 3, 3, 2, 10, 8, 8, 6, 12, 6, 6

Offset: 0

Antti Karttunen, Oct 27 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A001227, A163511, A366798 (rgs-transform).

Cf. also A324186, A366873.

A001227(n) = numdiv(n>>valuation(n, 2));
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));
A366797(n) = A001227(A163511(n));

a(n) = 2*A366873(n) - A324186(n).

A366800 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366799(i) = A366799(j) for all i, j >= 0, where A366799 is the number of divisors d of n that are not of the form 4k+2, as permuted by the Doudna sequence.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 3, 3, 2, 2, 4, 4, 3, 3, 4, 4, 2, 2, 4, 4, 4, 4, 5, 5, 3, 3, 5, 5, 4, 4, 6, 6, 2, 2, 4, 4, 4, 4, 5, 5, 4, 4, 7, 7, 5, 5, 7, 7, 3, 3, 5, 5, 5, 5, 8, 8, 4, 4, 7, 7, 6, 6, 5, 5, 2, 2, 4, 4, 4, 4, 5, 5, 4, 4, 7, 7, 5, 5, 7, 7, 4, 4, 7, 7, 7, 7, 9, 9, 5, 5, 9, 9, 7, 7, 10, 10, 3, 3, 5, 5, 5, 5, 8, 8

Offset: 0

Antti Karttunen, Oct 27 2023

nonn

Restricted growth sequence transform of A366799.

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A005940, A320111, A366799.

Cf. also A366798.

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); };
A320111(n) = sumdiv(n,d,(2!=(d%4)));
A366799(n) = A320111(A005940(1+n));
v366800 = rgs_transform(vector(1+up_to,n,A366799(n-1)));
A366800(n) = v366800[1+n];

cp's OEIS Frontend

A366874 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366873(i) = A366873(j) for all i, j >= 0, where A366873 is the average of number of and sum of odd divisors of n as permuted by A163511.

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A366797 Number of odd divisors permuted by A163511: a(n) = A001227(A163511(n)).

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A366800 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366799(i) = A366799(j) for all i, j >= 0, where A366799 is the number of divisors d of n that are not of the form 4k+2, as permuted by the Doudna sequence.

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PARI