%I #17 May 13 2017 03:46:35
%S 1,5,5,14,12,27,5,86,14,27,23,90,12,84,27,152,23,148,5,148,27,27,80,
%T 324,25,61,44,148,23,495,5,935,61,27,61,702,5,142,61,324,138,495,23,
%U 148,90,61,23,1426,14,265,27,90,467,324,27,430,27,61,80,2140,12,61,183,2144,61,495,23,607,27,495,23,2998,23,142,90,90,142,625,5,1426,226,27,467
%N Compound filter: a(n) = P(A046523(n), A046523(2n-1)), where P(n,k) is sequence A000027 used as a pairing function.
%H Antti Karttunen, <a href="/A286257/b286257.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%F a(n) = (1/2)*(2 + ((A046523(n)+A046523((2*n)-1))^2) - A046523(n) - 3*A046523((2*n)-1)).
%F a(n) = (1/2)*(2 + ((A046523(n)+A278223(n))^2) - A046523(n) - 3*A278223(n)).
%o (PARI)
%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 A286257(n) = (1/2)*(2 + ((A046523(n)+A046523((2*n)-1))^2) - A046523(n) - 3*A046523((2*n)-1));
%o for(n=1, 10000, write("b286257.txt", n, " ", A286257(n)));
%o (Scheme) (define (A286257 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A046523 (+ -1 n n))) 2) (- (A046523 n)) (- (* 3 (A046523 (+ -1 n n)))) 2)))
%o (Python)
%o from sympy import factorint
%o def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
%o def P(n):
%o f = factorint(n)
%o return sorted([f[i] for i in f])
%o def a046523(n):
%o x=1
%o while True:
%o if P(n) == P(x): return x
%o else: x+=1
%o def a(n): return T(a046523(n), a046523(2*n - 1)) # _Indranil Ghosh_, May 07 2017
%Y Cf. A000027, A046523, A278223, A286255, A286256, A286258.
%Y Cf. A005382 (gives the positions of 5's), A067756 (of 12's), A234098 (of 23's).
%K nonn
%O 1,2
%A _Antti Karttunen_, May 07 2017