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A354869 Positions of odd terms in A354866, the Dirichlet inverse of A122111.

%I A354869 #9 Jun 10 2022 11:09:38
%S A354869 1,4,8,9,18,25,27,32,36,49,50,54,64,72,75,98,100,108,121,125,147,150,
%T A354869 162,169,196,200,216,225,242,243,245,250,256,289,294,300,324,338,343,
%U A354869 361,363,375,392,441,450,484,486,490,500,507,512,529,576,578,588,600,605,675,676,686,722,726,729,735,750,841,845
%N A354869 Positions of odd terms in A354866, the Dirichlet inverse of A122111.
%C A354869 Apparently no squarefree terms after the initial 1.
%H A354869 Antti Karttunen, <a href="/A354869/b354869.txt">Table of n, a(n) for n = 1..8192; all terms <= 2^20</a>
%H A354869 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A354869 (PARI)
%o A354869 A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
%o A354869 memoA354866 = Map();
%o A354869 A354866(n) = if(1==n,1,my(v); if(mapisdefined(memoA354866,n,&v), v, v = -sumdiv(n,d,if(d<n,A122111(n/d)*A354866(d),0)); mapput(memoA354866,n,v); (v)));
%o A354869 A354868(n) = (A354866(n)%2);
%o A354869 isA354869(n) = A354868(n);
%Y A354869 Cf. A122111, A354866, A354868 (characteristic function).
%K A354869 nonn
%O A354869 1,2
%A A354869 _Antti Karttunen_, Jun 09 2022