A331182 -id:A331182 - cp's OEIS frontend

A331181 Number of values of k, 1 <= k <= n, with A033879(k) = A033879(n), where A033879(n) is the deficiency of n, 2n-sigma(n).

1, 2, 1, 3, 1, 1, 1, 4, 1, 2, 1, 1, 1, 2, 2, 5, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 6, 2, 2, 2, 1, 1, 2, 3, 1, 1, 3, 1, 3, 2, 1, 1, 1, 1, 1, 2, 3, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 4, 7, 2, 5, 1, 4, 2, 2, 1, 1, 1, 2, 2, 3, 2, 6, 1, 1, 2, 2, 1, 1, 1, 2, 1, 3, 1, 1, 2, 3, 3, 1, 3, 1, 1, 1, 3, 1, 1, 7, 1, 2, 3

Offset: 1

Antti Karttunen, Jan 11 2020

nonn

Ordinal transform of A033879, or equally, of A033880, or of A286449.

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

Cf. A000203, A033879, A033880, A286449.

Cf. also A331180, A331182.

b[_] = 0;
a[n_] := With[{t = 2 n - DivisorSigma[1, n]}, b[t] = b[t] + 1];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022 *)

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; };
A033879(n) = (2*n-sigma(n));
v331181 = ordinal_transform(vector(up_to,n,A033879(n)));
A331181(n) = v331181[n];

A331183 Number of values of k, 1 <= k <= n, with A323898(k) = A323898(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 4, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 1, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1, 4, 1, 1, 1, 2, 1, 6, 1, 1, 2, 3, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1

Offset: 1

Antti Karttunen, Jan 12 2020

nonn

Ordinal transform of A323898, or equally, of the ordered pair [A000120(n), A083254(n)].

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A000120, A083254, A323898.

Cf. also A331182, A331184.

up_to = 16384;
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; };
A083254(n) = (2*eulerphi(n)-n);
A323898aux(n) = [hammingweight(n), A083254(n)];
v331183 = ordinal_transform(vector(up_to,n,A323898aux(n)));
A331183(n) = v331183[n];

cp's OEIS Frontend

A331181 Number of values of k, 1 <= k <= n, with A033879(k) = A033879(n), where A033879(n) is the deficiency of n, 2n-sigma(n).

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