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%I A286149 #14 May 11 2017 13:43:12
%S A286149 1,5,8,14,17,34,30,44,19,51,68,103,93,72,196,152,155,103,192,132,72,
%T A286149 126,278,349,32,159,53,165,437,976,498,560,709,237,786,739,705,282,
%U A286149 159,402,863,660,948,243,337,384,1130,1273,49,132,1546,288,1433,349,126,459,282,567,1772,2761,1893,636,165,2144,2421,1921,2280,390,2707,2046,2558,2773,2703
%N A286149 Compound filter: a(n) = T(A046523(n), A109395(n)), where T(n,k) is sequence A000027 used as a pairing function.
%H A286149 Antti Karttunen, <a href="/A286149/b286149.txt">Table of n, a(n) for n = 1..10000</a>
%H A286149 MathWorld, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%F A286149 a(n) = (1/2)*(2 + ((A046523(n)+A109395(n))^2) - A046523(n) - 3*A109395(n)).
%t A286149 Table[(2 + (#1 + #2)^2 - #1 - 3 #2)/2 & @@ {Times @@ MapIndexed[ Prime[First@ #2]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]] - Boole[n == 1], Denominator[EulerPhi[n]/n]}, {n, 73}] (* _Michael De Vlieger_, May 04 2017 *)
%o A286149 (PARI)
%o A286149 A109395(n) = n/gcd(n, eulerphi(n));
%o A286149 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 A286149 A286149(n) = (1/2)*(2 + ((A046523(n)+A109395(n))^2) - A046523(n) - 3*A109395(n));
%o A286149 for(n=1, 10000, write("b286149.txt", n, " ", A286149(n)));
%o A286149 (Scheme) (define (A286149 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A109395 n)) 2) (- (A046523 n)) (- (* 3 (A109395 n))) 2)))
%o A286149 (Python)
%o A286149 from sympy import factorint, totient, gcd
%o A286149 def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
%o A286149 def P(n):
%o A286149     f = factorint(n)
%o A286149     return sorted([f[i] for i in f])
%o A286149 def a046523(n):
%o A286149     x=1
%o A286149     while True:
%o A286149         if P(n) == P(x): return x
%o A286149         else: x+=1
%o A286149 def a(n): return T(a046523(n), n/gcd(n, totient(n))) # _Indranil Ghosh_, May 05 2017
%Y A286149 Cf. A000027, A046523, A109395, A285729, A286142, A286143, A286144, A286152, A286154, A286160, A286161, A286162, A286163, A286164.
%K A286149 nonn
%O A286149 1,2
%A A286149 _Antti Karttunen_, May 04 2017

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