A294933 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.

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, 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, 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

Offset

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from exponents in factorization of n

Formula

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

Prog

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

Crossrefs

Cf. A294931, A294932.

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

Cf. A010057, A038148, A240231.

Sequence in context: A144368 A094438 A156098 * A015996 A256564 A092976

Adjacent sequences: A294930 A294931 A294932 * A294934 A294935 A294936

Keyword

nonn

Author

Antti Karttunen, Nov 11 2017

Status

approved