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A286161 Compound filter: a(n) = T(A001511(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function. 23

%I

%S 1,5,2,18,2,23,2,59,7,23,2,94,2,23,16,195,2,80,2,94,16,23,2,355,7,23,

%T 29,94,2,467,2,672,16,23,16,706,2,23,16,355,2,467,2,94,67,23,2,1331,7,

%U 80,16,94,2,302,16,355,16,23,2,1894,2,23,67,2422,16,467,2,94,16,467,2,2779,2,23,67,94,16,467,2,1331,121,23,2,1894,16,23,16,355,2,1832

%N Compound filter: a(n) = T(A001511(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function.

%H Antti Karttunen, <a href="/A286161/b286161.txt">Table of n, a(n) for n = 1..10000</a>

%H MathWorld, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

%F a(n) = (1/2)*(2 + ((A001511(n)+A046523(n))^2) - A001511(n) - 3*A046523(n)).

%o (PARI)

%o A001511(n) = (1+valuation(n,2));

%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 A286161(n) = (2 + ((A001511(n)+A046523(n))^2) - A001511(n) - 3*A046523(n))/2;

%o for(n=1, 10000, write("b286161.txt", n, " ", A286161(n)));

%o (Scheme) (define (A286161 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A046523 n)) 2) (- (A001511 n)) (- (* 3 (A046523 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 a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")

%o def a(n): return T(a001511(n), a046523(n)) # _Indranil Ghosh_, May 06 2017

%Y Cf. A000027, A001511, A046523, A286160, A286162, A286163, A286164, A286251.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 04 2017

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Last modified June 15 12:29 EDT 2021. Contains 345048 sequences. (Running on oeis4.)