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 A286358 Compound filter: a(n) = P(A286357(n), A161942(n)), where P(n,k) is sequence A000027 used as a pairing function. 5
 1, 4, 6, 22, 8, 13, 10, 106, 79, 47, 13, 39, 30, 19, 19, 466, 47, 742, 24, 233, 21, 58, 19, 139, 466, 233, 32, 49, 122, 70, 21, 1954, 26, 380, 26, 4096, 192, 139, 49, 1037, 233, 34, 81, 256, 782, 70, 26, 531, 1597, 4279, 70, 1227, 380, 157, 70, 157, 41, 1037, 139, 280, 498, 34, 124, 8002, 256, 83, 174, 2018, 34, 83, 70, 18916, 705, 1655, 531, 669, 34, 280, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Partitions natural numbers to the same equivalence classes as A000203. That is, for all i, j: a(i) = a(j) <=> A000203(i) = A000203(j). This follows because both A161942(n) and A286357(n) can be (are) defined as functions of A000203, and on the other hand, A000203(n) can be uniquely reconstructed from A161942(n) and A286357(n), thus from a(n). LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Pairing Function Index entries for sequences related to sigma(n) FORMULA a(n) = (1/2)*(2 + ((A286357(n)+A161942(n))^2) - A286357(n) - 3*A161942(n)). PROG (PARI) A001511(n) = (1+valuation(n, 2)); A000265(n) = (n >> valuation(n, 2)); A161942(n) = A000265(sigma(n)); A286357(n) = A001511(sigma(n)); A286358(n) = (1/2)*(2 + ((A286357(n)+A161942(n))^2) - A286357(n) - 3*A161942(n)); for(n=1, 10000, write("b286358.txt", n, " ", A286358(n))); (Scheme) (define (A286358 n) (* (/ 1 2) (+ (expt (+ (A286357 n) (A161942 n)) 2) (- (A286357 n)) (- (* 3 (A161942 n))) 2))) CROSSREFS Cf. A000027, A000203, A161942, A286034, A286260, A286357, A286359, A286360, A286460. Sequence in context: A282517 A227249 A002270 * A088228 A272309 A108636 Adjacent sequences: A286355 A286356 A286357 * A286359 A286360 A286361 KEYWORD nonn AUTHOR Antti Karttunen, May 10 2017 STATUS approved

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Last modified September 29 02:45 EDT 2023. Contains 365749 sequences. (Running on oeis4.)