A331181 - OEIS

%I #12 Jan 10 2022 06:51:54

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A331181/b331181.txt">Table of n, a(n) for n = 1..65537</a>

%t b[_] = 0;

%t a[n_] := With[{t = 2 n - DivisorSigma[1, n]}, b[t] = b[t] + 1];

%t Array[a, 105] (* _Jean-François Alcover_, Jan 10 2022 *)

%o (PARI)

%o up_to = 65537;

%o 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; };

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

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

%o A331181(n) = v331181[n];

%Y Cf. A000203, A033879, A033880, A286449.

%Y Cf. also A331180, A331182.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 11 2020