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A331180
Number of values of k, 1 <= k <= n, with A323910(k) = A323910(n), where A323910 is Dirichlet inverse of deficiency of n.
3
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 3, 1, 2, 1, 4, 1, 1, 1, 3, 1, 1, 2, 4, 1, 1, 1, 4, 5, 1, 1, 2, 1, 3, 1, 5, 1, 5, 1, 6, 1, 1, 1, 6, 1, 1, 2, 6, 1, 2, 1, 7, 1, 3, 1, 2, 1, 2, 8, 9, 1, 1, 1, 3, 2, 2, 1, 3, 1, 1, 1, 7, 1, 10, 1, 11, 2, 1, 2, 1, 1, 2, 2, 7, 1, 1, 1, 8, 2
OFFSET
1,8
COMMENTS
Ordinal transform of A323910.
LINKS
MATHEMATICA
f[n_] := 2 n - DivisorSigma[1, n];
A323910[n_] := A323910[n] = If[n == 1, 1, -Sum[f[n/d] A323910[d], {d, Most@Divisors[n]}]];
Module[{b}, b[_] = 0; a[n_] := With[{t = A323910[n]}, b[t] = b[t] + 1]];
Array[a, 105] (* Jean-François Alcover, Jan 12 2022 *)
PROG
(PARI)
up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -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.
A033879(n) = (2*n-sigma(n));
v331180 = ordinal_transform(DirInverse(vector(up_to, n, A033879(n))));
A331180(n) = v331180[n];
CROSSREFS
Cf. also A331178, A331181.
Sequence in context: A276153 A341348 A194606 * A126389 A278112 A286132
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 11 2020
STATUS
approved