login
A286358
Compound filter: a(n) = P(A286357(n), A161942(n)), where P(n,k) is sequence A000027 used as a pairing function.
4
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
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
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)))
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 10 2017
STATUS
approved