A286358 Compound filter: a(n) = P(A286357(n), A161942(n)), where P(n,k) is sequence A000027 used as a pairing function.

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

Author

Antti Karttunen, May 10 2017

Keywords

• nonn

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)

Crossrefs

Cf. A000027, A000203, A161942, A286034, A286260, A286357, A286359, A286360, A286460.

Programs

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)))

Formula

a(n) = (1/2)*(2 + ((A286357(n)+A161942(n))^2) - A286357(n) - 3*A161942(n)).