A286144 - OEIS

%I #11 May 05 2017 12:32:41

%S 1,2,3,5,10,8,21,14,21,14,55,19,78,27,36,44,136,34,171,44,78,65,253,

%T 53,210,90,171,90,406,63,465,152,210,152,300,103,666,189,300,152,820,

%U 103,903,230,300,275,1081,169,903,230,528,324,1378,208,820,324,666,434,1711,187,1830,495,666,560,1176,251,2211,560,990,324,2485,349,2628,702,820,702

%N Compound filter: a(n) = T(A000010(n), A257993(n)), where T(n,k) is sequence A000027 used as a pairing function.

%H Antti Karttunen, <a href="/A286144/b286144.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 + ((A000010(n)+A257993(n))^2) - A000010(n) - 3*A257993(n)).

%t Table[(2 + (#1 + #2)^2 - #1 - 3 #2)/2 & @@ {EulerPhi@ n, Module[{i = 1}, While[! CoprimeQ[Prime@ i, n], i++]; i]}, {n, 74}] (* _Michael De Vlieger_, May 04 2017 *)

%o (PARI)

%o A000010(n) = eulerphi(n);

%o A257993(n) = { for(i=1,n,if(n%prime(i),return(i))); }

%o A286144(n) = (2 + ((A000010(n)+A257993(n))^2) - A000010(n) - 3*A257993(n))/2;

%o for(n=1, 10000, write("b286144.txt", n, " ", A286144(n)));

%o (Scheme) (define (A286144 n) (* (/ 1 2) (+ (expt (+ (A000010 n) (A257993 n)) 2) (- (A000010 n)) (- (* 3 (A257993 n))) 2)))

%o (Python)

%o from sympy import prime, primepi, gcd, totient

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

%o def a053669(n):

%o     x=1

%o     while True:

%o         if gcd(prime(x), n) == 1: return prime(x)

%o         else: x+=1

%o def a257993(n): return primepi(a053669(n))

%o def a(n): return T(totient(n), a257993(n)) # _Indranil Ghosh_, May 05 2017

%Y Cf. A000010, A000027, A257993, A286142, A286143, A286152, A286160, A286161, A286162, A286163, A286164.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 04 2017