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A286455 Compound filter (smallest prime dividing n & prime signature of conjugated prime factorization): a(n) = P(A055396(n), A286621(n)), where P(n,k) is sequence A000027 used as a pairing function.

%I A286455 #12 Feb 16 2025 08:33:45
%S A286455 0,2,8,2,18,11,40,2,8,22,71,11,97,46,30,2,143,11,179,22,93,92,262,11,
%T A286455 18,121,8,46,335,154,417,2,212,211,69,11,540,254,302,22,679,326,794,
%U A286455 92,30,379,918,11,40,22,467,121,1051,11,234,46,530,529,1242,154,1344,631,93,2,744,704,1615,211,822,326,1790,11,1912,904,30,254,140,947,2167,22,8
%N A286455 Compound filter (smallest prime dividing n & prime signature of conjugated prime factorization): a(n) = P(A055396(n), A286621(n)), where P(n,k) is sequence A000027 used as a pairing function.
%C A286455 Note that as the other component of a(n) we use A286621 instead of A278221, because of latter sequence's unwieldy large terms.
%C A286455 For all i, j: a(i) = a(j) => A243055(i) = A243055(j).
%C A286455 For all i, j: a(i) = a(j) => A286470(i) = A286470(j).
%H A286455 Antti Karttunen, <a href="/A286455/b286455.txt">Table of n, a(n) for n = 1..10000</a>
%H A286455 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%F A286455 a(n) = (1/2)*(2 + ((A055396(n)+A286621(n))^2) - A055396(n) - 3*A286621(n)).
%o A286455 (Scheme) (define (A286455 n) (* (/ 1 2) (+ (expt (+ (A055396 n) (A286621 n)) 2) (- (A055396 n)) (- (* 3 (A286621 n))) 2)))
%Y A286455 Cf. A000027, A055396, A122111, A243055, A278221, A285334, A286621, A286454, A286456.
%K A286455 nonn
%O A286455 1,2
%A A286455 _Antti Karttunen_, May 14 2017