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A292587 Compound filter: a(n) = P(A001221(n), A292582(n)), where P(n,k) is sequence A000027 used as a pairing function. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

FORMULA

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

CROSSREFS

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

Sequence in context: A117920 A079617 A079616 * A097283 A296119 A300836

Adjacent sequences:  A292584 A292585 A292586 * A292588 A292589 A292590

KEYWORD

nonn,less

AUTHOR

Antti Karttunen, Sep 26 2017

STATUS

approved

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Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)