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A286592 Compound filter (prime signature & deficiency/abundance): a(n) = P(A046523(n), A286449(n)), where P(n,k) is sequence A000027 used as a pairing function.

%I A286592 #12 Feb 16 2025 08:33:45
%S A286592 1,3,5,10,8,42,17,36,40,27,30,183,47,34,51,136,57,243,80,288,72,177,
%T A286592 122,765,194,72,308,117,192,1020,212,528,142,259,196,1576,255,111,196,
%U A286592 1059,302,1020,327,103,202,471,380,2823,500,832,306,132,498,765,672,1564,747,786,668,4620,743,282,337,2080,502,1020,782,165,441,696,822,6288,905,747,1047,202
%N A286592 Compound filter (prime signature & deficiency/abundance): a(n) = P(A046523(n), A286449(n)), where P(n,k) is sequence A000027 used as a pairing function.
%C A286592 The lowermost conspicuous horizontal line in the scatter plot (at about log 3) is caused by value 1020, which corresponds to the prime signature 30 (p*q*r) and deficiency -12 packed together with the pairing function (as A002260(1020) = 30 and A004736(1020) = 16, A286449(24) = 16 and A033879(24) = -12). This value occurs in this sequence (at least) in the positions given by A138636, from its third term 30 onward.
%H A286592 Antti Karttunen, <a href="/A286592/b286592.txt">Table of n, a(n) for n = 1..10000</a>
%H A286592 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%F A286592 a(n) = (1/2)*(2 + ((A046523(n)+A286449(n))^2) - A046523(n) - 3*A286449(n)).
%o A286592 (Scheme) (define (A286592 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A286449 n)) 2) (- (A046523 n)) (- (* 3 (A286449 n))) 2)))
%Y A286592 Cf. A000027, A033879, A033880, A046523, A138636, A286449, A286593, A286595.
%K A286592 nonn
%O A286592 1,2
%A A286592 _Antti Karttunen_, May 21 2017