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A286595 Compound filter (2-adic valuation & deficiency/abundance): a(n) = P(A001511(n), A286449(n)), where P(n,k) is sequence A000027 used as a pairing function.

%I A286595 #9 Feb 16 2025 08:33:45
%S A286595 1,3,2,6,4,12,11,10,16,5,22,48,37,8,11,15,46,68,67,108,22,107,106,175,
%T A286595 137,30,154,18,172,138,191,21,67,173,106,256,232,57,106,329,277,138,
%U A286595 301,13,37,353,352,501,407,467,191,24,466,138,497,634,562,632,631,744,704,192,106,28,352,138,742,39,301,38,781,950,862,597,596,58,631,138,904,1133,407
%N A286595 Compound filter (2-adic valuation & deficiency/abundance): a(n) = P(A001511(n), A286449(n)), where P(n,k) is sequence A000027 used as a pairing function.
%H A286595 Antti Karttunen, <a href="/A286595/b286595.txt">Table of n, a(n) for n = 1..10000</a>
%H A286595 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%F A286595 a(n) = (1/2)*(2 + ((A001511(n)+A286449(n))^2) - A001511(n) - 3*A286449(n)).
%o A286595 (Scheme) (define (A286595 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A286449 n)) 2) (- (A001511 n)) (- (* 3 (A286449 n))) 2)))
%Y A286595 Cf. A000027, A001511, A033879, A033880, A286449, A286260, A286451, A286460, A286592, A286593.
%K A286595 nonn
%O A286595 1,2
%A A286595 _Antti Karttunen_, May 21 2017