A286251 - OEIS

%I #11 May 11 2017 10:27:27

%S 3,2,9,7,5,16,14,29,12,16,9,67,5,16,50,121,5,67,9,67,23,16,14,277,12,

%T 16,48,67,5,436,27,497,23,16,31,631,5,16,40,277,5,436,9,67,80,16,20,

%U 1129,12,67,31,67,5,277,40,277,23,16,9,1771,5,16,160,2017,23,436,9,67,23,436,14,2557,5,16,94,67,23,436,20,1129,138,16,9,1771,23,16,40,277,5

%N Compound filter: a(n) = P(A001511(1+n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function.

%H Antti Karttunen, <a href="/A286251/b286251.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(1+n)+A046523(n))^2) - A001511(1+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 A286251(n) = (2 + ((A001511(1+n)+A046523(n))^2) - A001511(1+n) - 3*A046523(n))/2;

%o for(n=1, 10000, write("b286251.txt", n, " ", A286251(n)));

%o (Scheme) (define (A286251 n) (* (/ 1 2) (+ (expt (+ (A001511 (+ 1 n)) (A046523 n)) 2) (- (A001511 (+ 1 n))) (- (* 3 (A046523 n))) 2)))

%o (Python)

%o from sympy import factorint

%o def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")

%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(a001511(n + 1), a046523(n)) # _Indranil Ghosh_, May 07 2017

%Y Cf. A000027, A001511, A046523, A286161, A286252, A286253, A286254.

%K nonn

%O 1,1

%A _Antti Karttunen_, May 07 2017