A366805 -id:A366805 - cp's OEIS frontend

A366803 Dirichlet convolution of Liouville's lambda with A342001 applied to Doudna sequence: a(n) = A347395(A005940(1+n)).

0, 1, 1, 1, 1, 3, 1, 2, 1, 5, 6, 3, 1, 2, 2, 2, 1, 7, 8, 5, 10, 14, 5, 5, 1, 2, 3, 2, 2, 4, 2, 3, 1, 11, 12, 7, 14, 20, 7, 9, 16, 34, 44, 14, 7, 9, 10, 5, 1, 2, 3, 2, 5, 5, 2, 3, 2, 6, 8, 4, 2, 3, 3, 3, 1, 13, 14, 11, 16, 32, 11, 13, 18, 54, 68, 20, 11, 13, 14, 9, 22, 76, 92, 34, 124, 92, 34, 22, 11, 13, 20, 9, 16

Offset: 0

Antti Karttunen, Oct 26 2023

nonn

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

Cf. A003415, A005940, A008836, A342001, A347395, A366805 (rgs-transform).

Cf. also A347396, A366795, A366801.

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));
A008836(n) = ((-1)^bigomega(n));
A347395(n) = sumdiv(n,d,A008836(n/d)*A342001(d));
A366803(n) = A347395(A005940(1+n));

A369067 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369066(i) = A369066(j) for all i, j >= 0.

Original entry on oeis.org

1, 2, 2, 1, 2, 3, 2, 3, 2, 4, 5, 1, 2, 6, 1, 7, 2, 8, 9, 1, 10, 11, 4, 9, 2, 6, 3, 1, 6, 1, 12, 5, 2, 13, 14, 1, 11, 15, 8, 11, 16, 17, 18, 1, 8, 19, 1, 20, 2, 6, 3, 1, 4, 4, 6, 4, 6, 5, 9, 1, 6, 8, 2, 20, 2, 21, 11, 1, 16, 22, 13, 15, 23, 24, 25, 1, 13, 21, 1, 26, 27, 28, 29, 1, 30, 29, 17, 31, 13, 21, 15, 1, 16

Offset: 0

Antti Karttunen, Jan 16 2024

nonn

Restricted growth sequence transform of A369066.

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

Cf. A005940, A008836, A083345, A369066, A369069.

Cf. also A366805 (compare the scatter plots).

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); };
A008836(n) = ((-1)^bigomega(n));
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369069(n) = sumdiv(n,d,A008836(n/d)*A083345(d));
A369066(n) = A369069(A005940(1+n));
v369067 = rgs_transform(vector(1+up_to,n,A369066(n-1)));
A369067(n) = v369067[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];

cp's OEIS Frontend

A366803 Dirichlet convolution of Liouville's lambda with A342001 applied to Doudna sequence: a(n) = A347395(A005940(1+n)).

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A369067 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369066(i) = A369066(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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