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%I #7 Jul 18 2017 11:46:10
%S 1,3,5,14,12,27,23,44,40,42,57,90,80,61,42,187,138,148,173,117,61,111,
%T 255,324,257,142,308,148,408,558,467,773,111,216,142,856,668,259,142,
%U 375,822,625,905,222,265,357,1083,1323,994,477,216,265,1380,844,306,430,259,534,1713,2013,1832,601,148,3145,142,771,2213,363,357
%N Compound filter (prime signature & Carmichael's lambda): a(n) = P(A046523(n), A002322(n)), where P(n,k) is sequence A000027 used as a pairing function.
%H Antti Karttunen, <a href="/A289622/b289622.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (1/2)*(2 + ((A046523(n)+A002322(n))^2) - A046523(n) - 3*A002322(n)).
%o (PARI)
%o A002322(n) = lcm(znstar(n)[2]); \\ This function from _Charles R Greathouse IV_, Aug 04 2012
%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from _Charles R Greathouse IV_, Aug 17 2011
%o A289622(n) = (1/2)*(2 + ((A046523(n)+A002322(n))^2) - A046523(n) - 3*A002322(n));
%Y Cf. A000027, A002322, A046523, A286160, A286360, A286573.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 16 2017
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