A292584 - OEIS

%I #25 Sep 27 2017 09:20:11

%S 1,2,5,2,8,5,13,2,4,8,19,5,25,13,9,2,32,4,41,8,12,19,51,5,16,25,5,13,

%T 72,9,85,2,18,32,14,4,98,41,26,8,112,12,128,19,8,51,145,5,46,16,33,25,

%U 180,5,18,13,49,72,200,9,220,85,13,2,24,18,242,32,60,14,265,4,288,98,8,41,19,26,313,8,4,112,339,12,33,128,62,19,365,8,25,51,84,145

%N Compound filter: a(n) = P(A292583(n), A292585(n)), where P(n,k) is sequence A000027 used as a pairing function.

%C From _Antti Karttunen_, Sep 25 2017: (Start)

%C Some of the sequences this filter matches to:

%C For all i, j: a(i) = a(j) => A053866(i) = A053866(j).

%C For all i, j: a(i) = a(j) => A061395(i) = A061395(j). (also A006530, etc.)

%C For all i, j: a(i) = a(j) => A292378(i) = A292378(j).

%C The latter two implications follow simply because:

%C   A001222(A278222(A292383(n))) = A000120(A292383(n)) = A292377(n)

%C and, similarly, for n > 1,

%C   A001222(A278222(A292385(n))) = A000120(A292381(n)) = A292375(n),

%C and the sum of A292375(n) and A292377(n) is A061395(n) [index of the largest prime dividing n], while A292378 has been defined as 1 + their difference.

%C The case A053866 follows because of the component A292583, see comments under that entry. (End)

%H Antti Karttunen, <a href="/A292584/b292584.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = (1/2)*(2 + ((A292583(n)+A292585(n))^2) - A292583(n) - 3*A292585(n)).

%Y Cf. A292383, A292385, A292583, A292585.

%Y Cf. also A006530, A061395, A292378 (some of the matched sequences).

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 20 2017