%I #16 May 09 2021 09:51:41

%S 0,1,2,1,3,4,5,2,3,6,7,4,8,9,10,5,11,6,12,7,13,14,15,8,9,16,10,11,17,

%T 18,19,12,20,21,22,13,23,24,25,14,26,27,28,15,16,29,30,17,18,19,31,20,

%U 32,21,33,22,34,35,36,23,37,38,24,25,39,40,41,26,42,43,44,27,45,46,28,29,47,48,49,30,31,50,51,32,52,53,54,33,55,34,56,35,57,58,59,36

%N a(1) = 0; for n > 1, if n is not squarefree, then a(n) = A057627(n), otherwise a(n) = A013928(n).

%C Each number n > 0 occurs exactly twice in this sequence, at the positions A005117(1+n) and A013929(n).

%H Antti Karttunen, <a href="/A284584/b284584.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1) = 0; for n > 1, if A008683(n) is 0 [when n is not squarefree], then a(n) = A057627(n), otherwise a(n) = A013928(n).

%o (Scheme) (define (A284584 n) (cond ((= 1 n) 0) ((zero? (A008683 n)) (A057627 n)) (else (A013928 n))))

%o (Python)

%o from sympy import mobius

%o from sympy.ntheory.factor_ import core

%o def a057627(n): return n - sum([mobius(k)**2 for k in range(1, n + 1)])

%o def a013928(n): return sum([1 for i in range(1, n) if core(i) == i])

%o def a(n):

%o if n==1: return 0

%o if core(n)==n: return a013928(n)

%o else: return a057627(n)

%o print([a(n) for n in range(1, 121)]) # _Indranil Ghosh_, Apr 17 2017

%Y Cf. A005117, A008683, A013928, A013929, A057627, A243343, A243345, A243347, A243352.

%Y Cf. A066136 (a similar sequence).

%K nonn

%O 1,3

%A _Antti Karttunen_, Apr 17 2017