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A347088 a(n) = A055155(n) - d(n), where A055155(n) = Sum_{d|n} gcd(d, n/d) and d(n) gives the number of divisors of n.

%I A347088 #13 Jul 29 2023 06:51:53
%S A347088 0,0,0,1,0,0,0,2,2,0,0,2,0,0,0,5,0,4,0,2,0,0,0,4,4,0,4,2,0,0,0,8,0,0,
%T A347088 0,11,0,0,0,4,0,0,0,2,4,0,0,10,6,8,0,2,0,8,0,4,0,0,0,4,0,0,4,15,0,0,0,
%U A347088 2,0,0,0,18,0,0,8,2,0,0,0,10,12,0,0,4,0,0,0,4,0,8,0,2,0,0,0,16,0,12,4,19,0,0,0,4,0
%N A347088 a(n) = A055155(n) - d(n), where A055155(n) = Sum_{d|n} gcd(d, n/d) and d(n) gives the number of divisors of n.
%H A347088 Antti Karttunen, <a href="/A347088/b347088.txt">Table of n, a(n) for n = 1..16384</a>
%F A347088 a(n) = A055155(n) - A000005(n).
%o A347088 (PARI)
%o A347088 A055155(n) = sumdiv(n, d, gcd(d, n/d)); \\ From A055155
%o A347088 A347088(n) = (A055155(n)-numdiv(n));
%o A347088 (Python)
%o A347088 from sympy import gcd, divisors, divisor_count
%o A347088 def A347088(n): return sum(gcd(d,n//d) for d in divisors(n,generator=True)) - divisor_count(n) # _Chai Wah Wu_, Aug 19 2021
%Y A347088 Cf. A000005, A005117 (positions of zeros), A055155, A347089.
%K A347088 nonn
%O A347088 1,8
%A A347088 _Antti Karttunen_, Aug 17 2021