A366803 -id:A366803 - cp's OEIS frontend

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

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];

A366795 a(n) = A344695(A005940(1+n)), where A344695(n) = gcd(psi(n), sigma(n)), and A005940 is the Doudna sequence.

Original entry on oeis.org

1, 3, 4, 1, 6, 12, 1, 3, 8, 18, 24, 4, 1, 3, 4, 1, 12, 24, 32, 6, 48, 72, 6, 12, 1, 3, 4, 1, 6, 12, 1, 3, 14, 36, 48, 8, 72, 96, 8, 18, 96, 144, 192, 24, 8, 18, 24, 4, 1, 3, 4, 1, 6, 12, 1, 3, 8, 18, 24, 8, 1, 3, 4, 1, 18, 42, 56, 12, 84, 144, 12, 24, 112, 216, 288, 32, 12, 24, 32, 6, 168, 288, 384, 48, 576, 576

Offset: 0

Antti Karttunen, Oct 26 2023

nonn

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

Cf. A005940, A344695, A366796 (rgs-transform).

Cf. also A346471, A366801, A366803.

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));

A369066 Dirichlet convolution of Liouville's lambda (A008836) with A083345, as reordered by the Doudna sequence.

Original entry on oeis.org

0, 1, 1, 0, 1, 3, 1, 3, 1, 5, 6, 0, 1, 2, 0, -1, 1, 7, 8, 0, 10, 14, 5, 8, 1, 2, 3, 0, 2, 0, 4, 6, 1, 11, 12, 0, 14, 20, 7, 14, 16, 34, 44, 0, 7, 9, 0, -3, 1, 2, 3, 0, 5, 5, 2, 5, 2, 6, 8, 0, 2, 7, 1, -3, 1, 13, 14, 0, 16, 32, 11, 20, 18, 54, 68, 0, 11, 13, 0, -5, 22, 76, 92, 0, 124, 92, 34, 36, 11, 13, 20, 0, 16

Offset: 0

Antti Karttunen, Jan 16 2024

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

Cf. A005940, A008836, A083345, A369067 (rgs-transform), A369069.

Cf. also A366803 (compare the scatter plots).

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));

a(n) = A369069(A005940(1+n)).

cp's OEIS Frontend

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

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A366795 a(n) = A344695(A005940(1+n)), where A344695(n) = gcd(psi(n), sigma(n)), and A005940 is the Doudna sequence.

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A369066 Dirichlet convolution of Liouville's lambda (A008836) with A083345, as reordered by the Doudna sequence.

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