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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A341533 A341741 A074723 * A175183 A189217 A183037
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 14 2017
STATUS
approved

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Last modified March 29 06:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)