A330746 - OEIS

%I #10 Jan 11 2020 21:50:18

%S 1,1,1,1,1,2,1,1,1,2,1,2,1,2,3,1,1,1,1,1,1,2,1,2,1,2,1,3,1,4,1,1,3,2,

%T 1,1,1,2,1,2,1,3,1,4,1,2,1,1,1,1,3,1,1,2,1,4,1,2,1,5,1,2,1,1,1,5,1,1,

%U 3,2,1,1,1,2,1,3,1,3,1,1,1,2,1,3,1,2,3,1,1,6,4,4,1,2,4,2,1,1,1,1,1,4,1,1,3

%N Number of values of k, 1 <= k <= n, with A017666(k) = A017666(n), where A017666(n) = n/gcd(n, sigma(n)).

%C Ordinal transform of A017666.

%H Antti Karttunen, <a href="/A330746/b330746.txt">Table of n, a(n) for n = 1..65537</a>

%F For all n >= 1, a(A014567(n)) = 1.

%F For all n >= 1, a(A007691(n)) = a(A159907(n)) = a(A245775(n)) = n.

%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 A017666(n) = (n/gcd(n, sigma(n)));

%o v330746 = ordinal_transform(vector(up_to, n, A017666(n)));

%o A330746(n) = v330746[n];

%Y Cf. A009194, A014567, A017666.

%Y A left inverse of following sequences: A007691, A159907, A245775.

%Y Cf. also A331175.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jan 11 2020