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A285710 Numbers n for which A000010(n) = A285699(n); positions of zeros in A285709.

%I A285710 #19 Apr 30 2021 06:02:21
%S A285710 1,2,3,4,5,6,7,8,9,11,13,14,16,17,19,21,23,25,27,28,29,31,32,37,41,43,
%T A285710 47,49,53,59,61,62,64,67,71,73,79,81,83,89,97,101,103,107,109,113,121,
%U A285710 124,125,127,128,131,137,139,149,151,157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,237
%N A285710 Numbers n for which A000010(n) = A285699(n); positions of zeros in A285709.
%C A285710 After a(1) = 1, also numbers n such that A051953(n) = A079277(n).
%H A285710 Antti Karttunen, <a href="/A285710/b285710.txt">Table of n, a(n) for n = 1..6672</a>
%t A285710 Flatten@ Position[#, 0] &@ 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, 240}] (* _Michael De Vlieger_, Apr 26 2017 *)
%o A285710 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A285710 (define A285710 (ZERO-POS 1 1 A285709))
%o A285710 (Python)
%o A285710 from sympy import divisors, totient
%o A285710 from sympy.ntheory.factor_ import core
%o A285710 def a007947(n): return max(i for i in divisors(n) if core(i) == i)
%o A285710 def a079277(n):
%o A285710     k=n - 1
%o A285710     while True:
%o A285710         if a007947(k*n) == a007947(n): return k
%o A285710         else: k-=1
%o A285710 def a285699(n): return 1 if n<2 else n - a079277(n)
%o A285710 print([n for n in range(1, 301) if totient(n) == a285699(n)]) # _Indranil Ghosh_, Apr 26 2017
%Y A285710 Positions of zeros in A285709.
%Y A285710 Cf. A000010, A051953, A079277, A208815, A285699.
%Y A285710 Cf. A000961 (a subsequence).
%K A285710 nonn
%O A285710 1,2
%A A285710 _Antti Karttunen_, Apr 26 2017