A292587 Compound filter: a(n) = P(A001221(n), A292582(n)), where P(n,k) is sequence A000027 used as a pairing function.

0, 1, 1, 2, 1, 3, 1, 4, 2, 3, 1, 5, 1, 3, 3, 7, 1, 5, 1, 5, 3, 3, 1, 8, 2, 3, 4, 5, 1, 6, 1, 11, 3, 3, 3, 23, 1, 3, 3, 8, 1, 6, 1, 5, 5, 3, 1, 12, 2, 5, 3, 5, 1, 8, 3, 8, 3, 3, 1, 9, 1, 3, 5, 22, 3, 6, 1, 5, 3, 6, 1, 38, 1, 3, 5, 5, 3, 6, 1, 12, 7, 3, 1, 9, 3, 3, 3, 8, 1, 9, 3, 5, 3, 3, 3, 17, 1, 5, 5, 23, 1, 6, 1, 8, 6

Offset: 1

Author

Antti Karttunen, Sep 26 2017

Keywords

• nonn
• less

Comments

This is essentially also a filter constructed from the runlengths of numbers of the form 4k+0 and the runlengths of numbers of the form 4k+2 encountered in trajectories of A005940-tree. See comments in A083399 and A292586.

For all i, j: A291757(i) = A291757(j) => a(i) = a(j), that is, this filter matches to a subset of the sequences matched by filter A291757.

Moreover, for all i, j: a(i) = a(j) <=> A101296(i) = A101296(j), thus the subset is exactly the sequences matched by A101296 (A046523). This follows because the prime signature of n can be recovered from the two components as A046523(n) = A046523(A003557(n)) * A292586(n) and also vice versa as A046523(A003557(n)) = A003557(A046523(n)).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000027, A001221, A003557, A005940, A046523, A101296, A291757, A292582, A292584, A292586, A292588.

Formula

a(n) = (1/2)*(2 + ((A001221(n) + A292582(n))^2) - A001221(n) - 3*A292582(n)).