cp's OEIS Frontend

A330753 Number of values of k, 1 <= k <= n, with A309639(k) = A309639(n), where A309639 gives the index of the least harmonic number whose denominator is divisible by n.

%I A330753 #9 Dec 30 2019 20:09:15
%S A330753 1,1,1,1,1,2,1,1,1,2,1,2,1,2,3,1,1,2,1,4,3,2,1,4,1,2,1,3,1,5,1,1,3,2,
%T A330753 4,5,1,2,3,2,1,6,1,4,7,2,1,2,1,2,3,4,1,2,5,3,3,2,1,6,1,2,8,1,5,6,1,4,
%U A330753 1,5,1,9,1,2,3,4,7,6,1,3,1,2,1,10,5,2,3,8,1,11,7,3,3,2,5,2,1,2,9,4,1,6,1,8,12
%N A330753 Number of values of k, 1 <= k <= n, with A309639(k) = A309639(n), where A309639 gives the index of the least harmonic number whose denominator is divisible by n.
%C A330753 Ordinal transform of A309639.
%C A330753 For all n, a(A000961(n)) = 1, but the sequence obtains value 1 also on other n that are not prime powers. In range 1..65537 these extra 1's occur at n = 69, 201, 407, 505, 576, 869, 1791, 5157, 9383, 9691, 10219, 10571, 10991, 12575, 12731, 13343, 13739, 14179, 14483, 14693, 16173, 16723, 23347, 24209, 26233, 26377, 37393, 44407, 46089, 53707, 62063.
%H A330753 Antti Karttunen, <a href="/A330753/b330753.txt">Table of n, a(n) for n = 1..65537</a>
%o A330753 (PARI)
%o A330753 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 A330753 v330753 = ordinal_transform(vector(up_to, n, A309639(n)));
%o A330753 A330753(n) = v330753[n];
%Y A330753 Cf. A000961, A309639.
%Y A330753 Cf. also A303759, A330754.
%K A330753 nonn
%O A330753 1,6
%A A330753 _Antti Karttunen_, Dec 30 2019