A286253 - OEIS

%I #9 May 07 2017 21:34:00

%S 0,1,8,1,9,1,25,1,5,1,26,1,27,1,17,1,35,1,53,1,5,1,75,1,9,1,8,1,65,1,

%T 131,1,5,1,13,1,90,1,12,1,104,1,134,1,5,1,186,1,14,1,8,1,152,1,18,1,5,

%U 1,188,1,189,1,30,1,9,1,229,1,5,1,273,1,252,1,8,1,14,1,347,1,5,1,323,1,9,1,12,1,324,1,19,1,5,1,31,1,350,1,8,1,377,1,462,1,5

%N Compound filter: a(n) = P(A055396(n), A001511(1+n)), where P(n,k) is sequence A000027 used as a pairing function.

%H Antti Karttunen, <a href="/A286253/b286253.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 + ((A055396(n)+A001511(1+n))^2) - A055396(n) - 3*A001511(1+n)).

%o (PARI)

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

%o A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])); \\ This function from _Charles R Greathouse IV_, Apr 23 2015

%o A286253(n) = (2 + ((A055396(n)+A001511(1+n))^2) - A055396(n) - 3*A001511(1+n))/2;

%o for(n=1, 10000, write("b286253.txt", n, " ", A286253(n)));

%o (Scheme) (define (A286253 n) (* (/ 1 2) (+ (expt (+ (A055396 n) (A001511 (+ 1 n))) 2) (- (A055396 n)) (- (* 3 (A001511 (+ 1 n)))) 2)))

%o (Python)

%o from sympy import primepi, isprime, primefactors

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

%o def a049084(n): return primepi(n)*(1*isprime(n))

%o def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))

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

%o def a(n): return T(a055396(n), a001511(n + 1)) # _Indranil Ghosh_, May 07 2017

%Y Cf. A000027, A001511, A055396, A286164, A286251, A286252, A286254.

%K nonn

%O 1,3

%A _Antti Karttunen_, May 07 2017