A366295 - OEIS

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

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of A349623.

LINKS

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

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.

A003961(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];

CROSSREFS

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

Cf. also A286603, A366294.

Sequence in context: A121701 A161759 A260643 * A300840 A243849 A286547

Adjacent sequences: A366292 A366293 A366294 * A366296 A366297 A366298

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 07 2023

STATUS

approved