A331181 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

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

MATHEMATICA

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 *)

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; };

A033879(n) = (2*n-sigma(n));

v331181 = ordinal_transform(vector(up_to, n, A033879(n)));

A331181(n) = v331181[n];

CROSSREFS

Cf. A000203, A033879, A033880, A286449.

Cf. also A331180, A331182.

Sequence in context: A331184 A333768 A306922 * A344593 A353278 A328917

Adjacent sequences: A331178 A331179 A331180 * A331182 A331183 A331184

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 11 2020

STATUS

approved