A366294 -id:A366294 - cp's OEIS frontend

A366295 Lexicographically earliest infinite sequence such that a(i) = a(j) => A349623(i) = A349623(j) for all i, j >= 1, where A349623 is the Dirichlet inverse of A064989(sigma(A003961(n))).

1, 2, 3, 4, 2, 5, 3, 6, 7, 1, 8, 9, 10, 5, 5, 11, 12, 13, 3, 14, 15, 16, 17, 18, 19, 15, 20, 9, 2, 3, 21, 22, 14, 23, 5, 24, 4, 5, 25, 26, 27, 10, 3, 28, 13, 29, 30, 31, 32, 33, 29, 34, 17, 35, 16, 18, 15, 1, 36, 37, 38, 39, 28, 40, 15, 4, 10, 41, 42, 3, 43, 44, 12, 14, 45, 9, 14, 30, 4, 46, 47, 48, 49, 50, 23, 5, 5

Offset: 1

Antti Karttunen, Oct 07 2023

nonn

Restricted growth sequence transform of A349623.

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

Cf. A000203, A003961, A064989, A326042, A349623.

Cf. also A286603, A366294.

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; };
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A326042(n) = A064989(sigma(A003961(n)));
v366295 = rgs_transform(DirInverseCorrect(vector(up_to,n,A326042(n))));
A366295(n) = v366295[n];

cp's OEIS Frontend

A366295 Lexicographically earliest infinite sequence such that a(i) = a(j) => A349623(i) = A349623(j) for all i, j >= 1, where A349623 is the Dirichlet inverse of A064989(sigma(A003961(n))).

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