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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Dec 30 2019

Keywords

• nonn

Comments

Ordinal transform of A309639.

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.

Links

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

Crossrefs

Cf. A000961, A309639.

Cf. also A303759, A330754.

Programs

PARI

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; };
v330753 = ordinal_transform(vector(up_to, n, A309639(n)));
A330753(n) = v330753[n];