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

Author

Antti Karttunen, May 14 2017

Keywords

• nonn

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

Crossrefs

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

Programs

Scheme

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

Formula

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