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A285709 a(n) = A000010(n) - A285699(n). 5

%I #24 May 08 2021 06:30:10

%S 0,0,0,0,0,0,0,0,0,2,0,1,0,0,2,0,0,4,0,4,0,4,0,2,0,2,0,0,0,5,0,0,14,

%T 14,14,8,0,12,12,8,0,6,0,8,6,8,0,4,0,10,8,4,0,12,10,17,6,2,0,10,0,0,

%U 22,0,8,18,0,28,2,18,0,16,0,26,10,24,32,18,0,16,0,22,0,21,4,20,50,16,0,15,30,16,48,16,2,17,0,8,42,20,0,26,0,8,24,10,0,24,0,30,42,34,0,30,-2

%N a(n) = A000010(n) - A285699(n).

%C The scatter plot has unusual "rays".

%H Antti Karttunen, <a href="/A285709/b285709.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000010(n) - A285699(n).

%F For n > 1, a(n) = (A000010(n) + A079277(n)) - n = A079277(n) - A051953(n).

%t Table[EulerPhi@ n - (n - If[n <= 2, n - 1, Module[{k = n - 2, e = Floor@ Log2@ n}, While[PowerMod[n, e, k] != 0, k--]; k]]), {n, 115}] (* _Michael De Vlieger_, Apr 26 2017 *)

%o (PARI)

%o A007947(n) = factorback(factorint(n)[, 1]); \\ From _Andrew Lelechenko_, May 09 2014

%o A079277(n) = { my(r); if((n > 1 && !bitand(n,(n-1))), (n/2), r=A007947(n); if(1==n,0,k = n-1; while(A007947(k*n) <> r, k = k-1); k)); };

%o A285709(n) = if(!n,n,(eulerphi(n)+A079277(n))-n);

%o (Scheme) (define (A285709 n) (- (A000010 n) (A285699 n)))

%o (Python)

%o from sympy import divisors, totient

%o from sympy.ntheory.factor_ import core

%o def a007947(n): return max(i for i in divisors(n) if core(i) == i)

%o def a079277(n):

%o k=n - 1

%o while True:

%o if a007947(k*n) == a007947(n): return k

%o else: k-=1

%o def a285699(n): return 1 if n<2 else n - a079277(n)

%o def a(n): return totient(n) - a285699(n)

%o print([a(n) for n in range(1, 116)]) # _Indranil Ghosh_, Apr 26 2017

%Y Cf. A000010, A007947, A051953, A079277, A285699, A285711.

%Y Cf. A285710 (positions of zeros), A208815 (of negative terms).

%K sign,look

%O 1,10

%A _Antti Karttunen_, Apr 26 2017

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)