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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))).
2
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
1,2
COMMENTS
Restricted growth sequence transform of A349623.
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 07 2023
STATUS
approved