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A366383
Lexicographically earliest infinite sequence such that a(i) = a(j) => A349915(i) = A349915(j) for all i, j >= 1, where A349915 is Dirichlet inverse of arithmetic mean between the number of odd divisors and their sum.
2
1, 2, 3, 4, 5, 6, 7, 4, 1, 8, 9, 4, 10, 11, 12, 4, 13, 2, 14, 4, 15, 16, 17, 4, 2, 18, 2, 4, 19, 13, 20, 4, 21, 12, 22, 4, 23, 24, 25, 4, 26, 27, 28, 4, 29, 30, 31, 4, 7, 1, 32, 4, 33, 1, 25, 4, 34, 21, 35, 4, 36, 37, 29, 4, 38, 19, 39, 4, 40, 41, 42, 4, 43, 38, 11, 4, 38, 44, 45, 4, 29, 32, 46, 4, 34, 47, 48, 4, 49
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
A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
v366383 = rgs_transform(DirInverseCorrect(vector(up_to, n, A113415(n))));
A366383(n) = v366383[n];
CROSSREFS
Sequence in context: A278059 A329606 A115871 * A366382 A138221 A038388
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2023
STATUS
approved