A366802 -id:A366802 - cp's OEIS frontend

A366801 Arithmetic derivative without its inherited divisor applied to the Doudna sequence: a(n) = A342001(A005940(1+n)).

0, 1, 1, 2, 1, 5, 2, 3, 1, 7, 8, 8, 2, 7, 3, 4, 1, 9, 10, 12, 12, 31, 13, 11, 2, 9, 11, 10, 3, 9, 4, 5, 1, 13, 14, 16, 16, 41, 17, 17, 18, 59, 71, 46, 19, 41, 18, 14, 2, 11, 13, 14, 17, 37, 16, 13, 3, 11, 14, 12, 4, 11, 5, 6, 1, 15, 16, 24, 18, 61, 25, 23, 20, 87, 103, 62, 27, 55, 24, 22, 24, 113, 131, 94, 167, 247

Offset: 0

Antti Karttunen, Oct 24 2023

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

Cf. A003415, A005940, A342001, A344026, A366802 (rgs-transform).

Cf. also A342002.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A342001(n) = (A003415(n) / A003557(n));
A366801(n) = A342001(A005940(1+n));

A366805 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366803(i) = A366803(j) for all i, j >= 0.

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 2, 4, 2, 5, 6, 3, 2, 4, 4, 4, 2, 7, 8, 5, 9, 10, 5, 5, 2, 4, 3, 4, 4, 11, 4, 3, 2, 12, 13, 7, 10, 14, 7, 15, 16, 17, 18, 10, 7, 15, 9, 5, 2, 4, 3, 4, 5, 5, 4, 3, 4, 6, 8, 11, 4, 3, 3, 3, 2, 19, 10, 12, 16, 20, 12, 19, 21, 22, 23, 14, 12, 19, 10, 15, 24, 25, 26, 17, 27, 26, 17, 24, 12, 19, 14, 15

Offset: 0

Antti Karttunen, Oct 26 2023

Restricted growth sequence transform of A366803.

The scatter plot has quite interesting structure.

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

Cf. A003415, A005940, A008836, A347395, A366803.

Cf. also A366796, A366802.

\\ Needs also program from A366803:
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; };
v366805 = rgs_transform(vector(1+up_to,n,A366803(n-1)));
A366805(n) = v366805[1+n];

A366796 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366795(i) = A366795(j) for all i, j >= 0.

Original entry on oeis.org

1, 2, 3, 1, 4, 5, 1, 2, 6, 7, 8, 3, 1, 2, 3, 1, 5, 8, 9, 4, 10, 11, 4, 5, 1, 2, 3, 1, 4, 5, 1, 2, 12, 13, 10, 6, 11, 14, 6, 7, 14, 15, 16, 8, 6, 7, 8, 3, 1, 2, 3, 1, 4, 5, 1, 2, 6, 7, 8, 6, 1, 2, 3, 1, 7, 17, 18, 5, 19, 15, 5, 8, 20, 21, 22, 9, 5, 8, 9, 4, 23, 22, 24, 10, 25, 25, 10, 11, 5, 8, 9, 4, 10, 11, 4, 5, 1

Offset: 0

Antti Karttunen, Oct 26 2023

nonn

Restricted growth sequence transform of A366795.

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

Cf. A005940, A344695, A366795.

Cf. also A366802, A366805.

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; };
A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A344695(n) = gcd(sigma(n), A001615(n));
A366795(n) = A344695(A005940(1+n));
v366796 = rgs_transform(vector(1+up_to,n,A366795(n-1)));
A366796(n) = v366796[1+n];

A369065 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344026(i) = A344026(j) for all i, j >= 0.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 10, 11, 12, 13, 2, 14, 10, 15, 6, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 2, 27, 19, 13, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 2, 55, 9, 56, 31, 57, 23, 34, 58, 59, 60, 61, 62, 63, 50, 64, 15, 65, 66

Offset: 0

Antti Karttunen, Jan 16 2024

nonn

Restricted growth sequence transform of A344026, i.e., of the arithmetic derivative (A003415) as reordered by the Doudna sequence (A005940).

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

Cf. A003415, A005940, A344026.

Cf. also A366802, 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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A344026(n) = A003415(A005940(1+n));
v369065 = rgs_transform(vector(1+up_to,n,A344026(n-1)));
A369065(n) = v369065[1+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

A366801 Arithmetic derivative without its inherited divisor applied to the Doudna sequence: a(n) = A342001(A005940(1+n)).

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A366805 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366803(i) = A366803(j) for all i, j >= 0.

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A366796 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366795(i) = A366795(j) for all i, j >= 0.

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A369065 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344026(i) = A344026(j) for all i, j >= 0.

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

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