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A378223 Inverse Möbius transform of A345182.

%I A378223 #12 Nov 30 2024 23:46:12
%S A378223 1,1,2,2,2,4,2,4,4,4,2,10,2,4,6,8,2,12,2,10,6,4,2,24,4,4,8,10,2,20,2,
%T A378223 16,6,4,6,36,2,4,6,24,2,20,2,10,16,4,2,56,4,12,6,10,2,32,6,24,6,4,2,
%U A378223 62,2,4,16,32,6,20,2,10,6,20,2,100,2,4,16,10,6,20,2,56,16,4,2,62,6,4,6,24,2,72,6,10,6,4,6
%N A378223 Inverse Möbius transform of A345182.
%C A378223 Apparently the Dirichlet convolution of A002131 and A323910. - _Antti Karttunen_, Nov 30 2024
%H A378223 Antti Karttunen, <a href="/A378223/b378223.txt">Table of n, a(n) for n = 1..20000</a>
%F A378223 a(n) = Sum_{d|n} A345182(d).
%F A378223 For n > 2, a(n) = 2*A345182(n).
%o A378223 (PARI)
%o A378223 memoA345182 = Map();
%o A378223 A345182(n) = if(n<=2, n%2, my(v); if(mapisdefined(memoA345182,n,&v), v, v = sumdiv(n,d,if(d<n,A345182(d),0)); mapput(memoA345182,n,v); (v)));
%o A378223 A378223(n) = sumdiv(n,d,A345182(d));
%o A378223 (PARI)
%o A378223 up_to = 20000;
%o A378223 A378223list(up_to_n) = { my(v=vector(up_to_n)); v[1] = 1; v[2] = 0; for(n=3,up_to_n,v[n] = 1+sumdiv(n,d,(d<n)*v[d])); v[2]++; (v); };
%o A378223 v378223 = A378223list(up_to);
%o A378223 A378223(n) = v378223[n];
%Y A378223 Cf. A002131, A323910, A345182, A378224 (Dirichlet inverse).
%Y A378223 Cf. also A067824.
%Y A378223 Odd bisection is not equal to A278223.
%K A378223 nonn
%O A378223 1,3
%A A378223 _Antti Karttunen_, Nov 25 2024