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A286142 Compound filter: a(n) = T(A257993(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function. 9

%I

%S 1,5,2,12,2,31,2,38,7,23,2,94,2,23,16,138,2,94,2,80,16,23,2,328,7,23,

%T 29,80,2,532,2,530,16,23,16,706,2,23,16,302,2,499,2,80,67,23,2,1228,7,

%U 80,16,80,2,328,16,302,16,23,2,1957,2,23,67,2082,16,499,2,80,16,467,2,2704,2,23,67,80,16,499,2,1178,121,23,2,1894,16,23,16,302,2,1957,16

%N Compound filter: a(n) = T(A257993(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function.

%H Antti Karttunen, <a href="/A286142/b286142.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 + ((A257993(n)+A046523(n))^2) - A257993(n) - 3*A046523(n)).

%t Table[(2 + (#1 + #2)^2 - #1 - 3 #2)/2 - Boole[n == 1] & @@ {Module[{i = 1}, While[! CoprimeQ[Prime@ i, n], i++]; i], Times @@ MapIndexed[ Prime[First@ #2]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]]}, {n, 92}] (* _Michael De Vlieger_, May 04 2017 *)

%o (PARI)

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

%o A286142(n) = (1/2)*(2 + ((A257993(n)+A046523(n))^2) - A257993(n) - 3*A046523(n));

%o for(n=1, 10000, write("b286142.txt", n, " ", A286142(n)));

%o (Scheme) (define (A286142 n) (* (/ 1 2) (+ (expt (+ (A257993 n) (A046523 n)) 2) (- (A257993 n)) (- (* 3 (A046523 n))) 2)))

%o (Python)

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

%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 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(a257993(n), a046523(n)) # _Indranil Ghosh_, May 05 2017

%Y Cf. A000027, A046523, A257993, A286144, A286160, A286161, A286162, A286163, A286164.

%Y Differs from A286143 for the first time at n=24, where a(24) = 328, while A286143(24) = 355.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 04 2017

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)