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A365430 a(n) = A156552(gcd(n, A005940(n))), and A156552 is the inverse of offset-0 version of Doudna-sequence A005940.

%I A365430 #11 Sep 07 2023 16:10:02
%S A365430 0,1,2,3,4,5,0,7,0,9,0,11,0,1,2,15,0,1,0,19,8,1,0,23,0,1,2,3,0,5,0,31,
%T A365430 0,1,0,3,0,1,2,39,0,17,0,3,4,1,0,47,0,1,2,3,0,5,4,7,0,1,0,11,0,1,6,63,
%U A365430 0,1,0,3,0,1,0,7,0,1,10,3,16,5,0,79,0,1,0,35,4,1,2,7,0,9,8,3,0,1,4,95,0,1,34,3
%N A365430 a(n) = A156552(gcd(n, A005940(n))), and A156552 is the inverse of offset-0 version of Doudna-sequence A005940.
%H A365430 Antti Karttunen, <a href="/A365430/b365430.txt">Table of n, a(n) for n = 1..16384</a>
%F A365430 a(n) = A156552(A364500(n)).
%F A365430 For all n >= 1, a(n) <= n-1 and A341520(a(n), A365432(n)) = n-1.
%o A365430 (PARI)
%o A365430 A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A365430 A364500(n) = { my(orgn=n,p=2,rl=0,z=1); n--; while(n, if(!(n%2), p=nextprime(1+p), rl++; if(1==(n%4), z *= p^min(rl,valuation(orgn,p)); rl=0)); n>>=1); (z); };
%o A365430 A365430(n) = A156552(A364500(n));
%Y A365430 Cf. A005940, A364500, A341520, A365432.
%K A365430 nonn
%O A365430 1,3
%A A365430 _Antti Karttunen_, Sep 07 2023