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A286260 Compound filter: a(n) = P(A001511(n), A161942(n)), where P(n,k) is sequence A000027 used as a pairing function.

%I A286260 #9 Feb 16 2025 08:33:44
%S A286260 1,8,1,39,4,8,1,157,79,47,4,39,22,8,4,600,37,782,11,256,1,47,4,157,
%T A286260 466,233,11,39,106,47,1,2284,4,380,4,4281,172,122,22,1132,211,8,56,
%U A286260 256,742,47,4,600,1597,4373,37,1278,352,122,37,157,11,1037,106,256,466,8,79,8785,211,47,137,2083,4,47,37,19507,667,1655,466,669,4,233,11,4661,7261
%N A286260 Compound filter: a(n) = P(A001511(n), A161942(n)), where P(n,k) is sequence A000027 used as a pairing function.
%H A286260 Antti Karttunen, <a href="/A286260/b286260.txt">Table of n, a(n) for n = 1..16384</a>
%H A286260 MathWorld, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%F A286260 a(n) = (1/2)*(2 + ((A001511(n)+A161942(n))^2) - A001511(n) - 3*A161942(n)).
%o A286260 (PARI)
%o A286260 A001511(n) = (1+valuation(n,2));
%o A286260 A000265(n) = (n >> valuation(n, 2));
%o A286260 A161942(n) = A000265(sigma(n));
%o A286260 A286260(n) = (2 + ((A001511(n)+A161942(n))^2) - A001511(n) - 3*A161942(n))/2;
%o A286260 for(n=1, 16384, write("b286260.txt", n, " ", A286260(n)));
%o A286260 (Scheme) (define (A286260 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A161942 n)) 2) (- (A001511 n)) (- (* 3 (A161942 n))) 2)))
%o A286260 (Python)
%o A286260 from sympy import factorint, divisors, divisor_sigma
%o A286260 def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
%o A286260 def a000265(n): return max(list(filter(lambda i: i%2 == 1, divisors(n))))
%o A286260 def a161942(n): return a000265(divisor_sigma(n))
%o A286260 def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")
%o A286260 def a(n): return T(a001511(n), a161942(n)) # _Indranil Ghosh_, May 07 2017
%Y A286260 Cf. A000027, A001511, A161942, A286161, A286162, A286259, A286034.
%K A286260 nonn
%O A286260 1,2
%A A286260 _Antti Karttunen_, May 07 2017