A286455 Compound filter (smallest prime dividing n & prime signature of conjugated prime factorization): a(n) = P(A055396(n), A286621(n)), where P(n,k) is sequence A000027 used as a pairing function.

0, 2, 8, 2, 18, 11, 40, 2, 8, 22, 71, 11, 97, 46, 30, 2, 143, 11, 179, 22, 93, 92, 262, 11, 18, 121, 8, 46, 335, 154, 417, 2, 212, 211, 69, 11, 540, 254, 302, 22, 679, 326, 794, 92, 30, 379, 918, 11, 40, 22, 467, 121, 1051, 11, 234, 46, 530, 529, 1242, 154, 1344, 631, 93, 2, 744, 704, 1615, 211, 822, 326, 1790, 11, 1912, 904, 30, 254, 140, 947, 2167, 22, 8

Offset

1,2

Comments

Note that as the other component of a(n) we use A286621 instead of A278221, because of latter sequence's unwieldy large terms.

For all i, j: a(i) = a(j) => A243055(i) = A243055(j).

For all i, j: a(i) = a(j) => A286470(i) = A286470(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Pairing Function

Formula

a(n) = (1/2)*(2 + ((A055396(n)+A286621(n))^2) - A055396(n) - 3*A286621(n)).

Prog

(Scheme) (define (A286455 n) (* (/ 1 2) (+ (expt (+ (A055396 n) (A286621 n)) 2) (- (A055396 n)) (- (* 3 (A286621 n))) 2)))

Crossrefs

Cf. A000027, A055396, A122111, A243055, A278221, A285334, A286621, A286454, A286456.

Sequence in context: A341533 A341741 A074723 * A175183 A189217 A183037

Adjacent sequences: A286452 A286453 A286454 * A286456 A286457 A286458

Keyword

nonn

Author

Antti Karttunen, May 14 2017

Status

approved