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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.
3
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
1,6
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
PROG
(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];
CROSSREFS
Cf. also A303759, A330754.
Sequence in context: A276781 A303759 A330754 * A082068 A300360 A300396
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 30 2019
STATUS
approved