A286388 - OEIS

%I #7 May 14 2017 15:54:39

%S 0,1,4,3,2,6,7,10,9,15,4,21,2,28,41,36,2,45,4,55,35,66,7,78,20,91,64,

%T 105,2,120,16,136,77,153,43,171,2,190,133,210,2,231,4,253,135,276,11,

%U 300,35,325,188,351,2,378,102,406,209,435,4,465,2,496,372,528,104,561,4,595,299,630,7,666,2,703,376,741,77,780,11,820,405,861,4,903,170,946

%N Compound filter ("discard the smallest prime factor" & "number of trailing 1-bits in base-2"): a(n) = P(A032742(n), A001511(1+n)), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = 0.

%H Antti Karttunen, <a href="/A286388/b286388.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1) = 0, for n > 1, a(n) = (1/2)*(2 + ((A032742(n)+A001511(1+n))^2) - A032742(n) - 3*A001511(1+n)).

%o (Scheme) (define (A286388 n) (if (= 1 n) 0 (* (/ 1 2) (+ (expt (+ (A032742 n) (A001511 (+ 1 n))) 2) (- (A032742 n)) (- (* 3 (A001511 (+ 1 n)))) 2))))

%o (Python)

%o from sympy import divisors

%o def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

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

%o def a(n): return 0 if n==1 else T(divisors(n)[-2], a001511(n + 1)) # _Indranil Ghosh_, May 14 2017

%Y Cf. A000027, A001511, A032742, A286379, A286386.

%K nonn

%O 1,3

%A _Antti Karttunen_, May 13 2017