A294933 - OEIS

%I #12 Nov 13 2017 13:23:19

%S 1,2,2,3,2,7,2,4,3,7,2,5,2,7,7,16,2,5,2,5,7,7,2,16,3,7,4,5,2,29,2,8,7,

%T 7,7,10,2,7,7,16,2,29,2,5,5,7,2,67,3,5,7,5,2,16,7,16,7,7,2,12,2,7,5,6,

%U 7,29,2,5,7,29,2,8,2,7,5,5,7,29,2,67,16,7,2,12,7,7,7,16,2,12,7,5,7,7,7,23,2,5,5,10,2,29,2,16,29,7,2,8,2,29,7,67

%N Compound filter related to base-3 expansion of the exponents in prime factorization of n: a(n) = P(A294932(n), A294931(n)), where P(n,k) is sequence A000027 used as a pairing function.

%C For all i, j: a(i) = a(j) => A038148(i) = A038148(j).

%H Antti Karttunen, <a href="/A294933/b294933.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = (1/2)*(2 + ((A294932(n) + A294931(n))^2) - A294932(n) - 3*A294931(n)).

%o (define (A294933 n) (* 1/2 (+ (expt (+ (A294932 n) (A294931 n)) 2) (- (A294932 n)) (- (* 3 (A294931 n))) 2)))

%Y Cf. A294931, A294932.

%Y Cf. also A293225, A293226 and A293442 (analogous filter for base-2).

%Y Cf. A010057, A038148, A240231.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 11 2017