|
%I #24 Apr 30 2021 06:06:24
%S 1,1,2,2,4,2,6,4,6,2,10,3,12,6,6,8,16,2,18,4,12,6,22,6,20,10,18,12,28,
%T 3,30,16,6,2,10,4,36,6,12,8,40,6,42,12,18,14,46,12,42,10,24,20,52,6,
%U 30,7,30,26,58,6,60,30,14,32,40,2,66,4,42,6,70,8,72,10,30,12,28,6,78,16,54,18,82,3,60,22,6,24,88,9,42,28,12,30,70,15,96,34,18,20
%N a(1) = 1; for n > 1, a(n) = n - A079277(n).
%C The scatter plot has unusual "rays".
%H Antti Karttunen, <a href="/A285699/b285699.txt">Table of n, a(n) for n = 1..10000</a>
%F a(1) = 1; for n > 1, a(n) = n - A079277(n).
%F Other identities. For all n >= 1:
%F a(A285710(n)) = A000010(A285710(n)). [A285710 gives all such matches.]
%t Table[n - If[n <= 2, n - 1, Module[{k = n - 2, e = Floor@ Log2@ n}, While[PowerMod[n, e, k] != 0, k--]; k]], {n, 100}] (* _Michael De Vlieger_, Apr 26 2017 *)
%o (Scheme) (define (A285699 n) (if (= 1 n) n (- n (A079277 n))))
%o (Python)
%o from sympy import divisors
%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 a(n): return 1 if n<2 else n - a079277(n)
%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Apr 26 2017
%Y Cf. A000010, A079277, A285710.
%K nonn,look
%O 1,3
%A _Antti Karttunen_, Apr 26 2017
|
