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A286160 Compound filter: a(n) = T(A000010(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function. 18

%I

%S 1,2,5,12,14,23,27,59,42,40,65,109,90,61,86,261,152,142,189,179,148,

%T 115,275,473,273,148,318,265,434,674,495,1097,320,226,430,1093,702,

%U 271,430,757,860,832,945,485,619,373,1127,1969,1032,485,698,619,1430,838,1030,1105,856,556,1769,2791,1890,625,1117,4497,1426,1196,2277,935,1220

%N Compound filter: a(n) = T(A000010(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function.

%H Antti Karttunen, <a href="/A286160/b286160.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)+A046523(n))^2) - A000010(n) - 3*A046523(n)).

%o (PARI)

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

%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 A286160(n) = (2 + ((A000010(n)+A046523(n))^2) - A000010(n) - 3*A046523(n))/2;

%o for(n=1, 10000, write("b286160.txt", n, " ", A286160(n)));

%o (Scheme)

%o (define (A286160 n) (* (/ 1 2) (+ (expt (+ (A000010 n) (A046523 n)) 2) (- (A000010 n)) (- (* 3 (A046523 n))) 2)))

%o (Python)

%o from sympy import factorint, totient

%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 a(n): return T(totient(n), a046523(n)) # _Indranil Ghosh_, May 06 2017

%Y Cf. A000010, A000027, A046523, A286161, A286162, A286163, A286164.

%Y Cf. for example A061468 (one of the sequences this matches with).

%K nonn

%O 1,2

%A _Antti Karttunen_, May 04 2017

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Last modified July 30 04:47 EDT 2021. Contains 346348 sequences. (Running on oeis4.)