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A366382
Lexicographically earliest infinite sequence such that a(i) = a(j) => A349134(i) = A349134(j) for all i, j >= 1, where A349134 is Dirichlet inverse of Kimberling's paraphrases.
1
1, 2, 3, 4, 5, 6, 7, 4, 2, 8, 9, 4, 10, 11, 11, 4, 12, 1, 13, 4, 14, 15, 16, 4, 7, 17, 3, 4, 18, 7, 19, 4, 17, 20, 15, 4, 21, 22, 23, 4, 24, 25, 26, 4, 8, 27, 28, 4, 12, 11, 22, 4, 29, 6, 23, 4, 30, 31, 32, 4, 33, 34, 11, 4, 20, 10, 35, 4, 36, 9, 37, 4, 38, 39, 23, 4, 20, 40, 41, 4, 7, 42, 43, 4, 30, 44, 34, 4, 45, 5, 22
OFFSET
1,2
LINKS
PROG
(PARI)
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(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v
A003602(n) = (1+(n>>valuation(n, 2)))/2;
v366382 = rgs_transform(DirInverseCorrect(vector(up_to, n, A003602(n))));
A366382(n) = v366382[n];
CROSSREFS
Sequence in context: A329606 A115871 A366383 * A138221 A038388 A366392
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2023
STATUS
approved