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A354876 Sum of A344005 and its Dirichlet inverse, where A344005(n) is the smallest positive m such that n divides the oblong number m*(m+1).

%I A354876 #9 Jun 12 2022 22:53:30
%S A354876 2,0,0,1,0,4,0,5,4,8,0,10,0,12,16,15,0,12,0,20,24,20,0,12,16,24,24,30,
%T A354876 0,-6,0,35,40,32,48,20,0,36,48,20,0,-12,0,50,36,44,0,9,36,32,64,60,0,
%U A354876 28,80,32,72,56,0,-63,0,60,48,71,96,-18,0,80,88,-20,0,32,0,72,40,90,120,-24,0,10,88,80,0,-98,128
%N A354876 Sum of A344005 and its Dirichlet inverse, where A344005(n) is the smallest positive m such that n divides the oblong number m*(m+1).
%H A354876 Antti Karttunen, <a href="/A354876/b354876.txt">Table of n, a(n) for n = 1..20000</a>
%F A354876 a(n) = A344005(n) + A354875(n).
%F A354876 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A344005(d) * A354875(n/d).
%o A354876 (PARI)
%o A354876 A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
%o A354876 memoA354875 = Map();
%o A354876 A354875(n) = if(1==n,1,my(v); if(mapisdefined(memoA354875,n,&v), v, v = -sumdiv(n,d,if(d<n,A344005(n/d)*A354875(d),0)); mapput(memoA354875,n,v); (v)));
%o A354876 A354876(n) = (A344005(n)+A354875(n));
%Y A354876 Cf. A344005, A354875.
%Y A354876 Cf. also A345065.
%K A354876 sign
%O A354876 1,1
%A A354876 _Antti Karttunen_, Jun 12 2022