A347088 - OEIS

%I #13 Jul 29 2023 06:51:53

%S 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 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 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 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 Antti Karttunen, <a href="/A347088/b347088.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = A055155(n) - A000005(n).

%o (PARI)

%o A055155(n) = sumdiv(n, d, gcd(d, n/d)); \\ From A055155

%o A347088(n) = (A055155(n)-numdiv(n));

%o (Python)

%o from sympy import gcd, divisors, divisor_count

%o 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 Cf. A000005, A005117 (positions of zeros), A055155, A347089.

%K nonn

%O 1,8

%A _Antti Karttunen_, Aug 17 2021