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%I #13 Jun 04 2024 10:52:48
%S 0,1,1,2,1,1,1,3,2,7,1,1,1,1,8,4,1,1,1,1,2,1,1,1,2,1,3,1,1,1,1,5,2,1,
%T 12,2,1,1,8,1,1,1,1,1,1,1,1,1,2,1,4,1,1,1,8,1,2,1,1,2,1,1,1,6,6,1,1,1,
%U 2,1,1,1,1,1,1,1,6,1,1,1,4,1,1,2,2,1,8,1,1,1,20,1,2,1,12,1,1,1,1,14,1,1,1,1,1
%N a(n) is the greatest common divisor of A001414(n), A003415(n), and A276085(n).
%C All sequences that give the positions of multiples of some natural number k in this sequence are closed under multiplication because the constituent sequences A001414, A003415, and A276085 also have the same property.
%C A345452 gives the positions of even terms in this sequence, because it gives them for A373362, and because for A373145 and A373364 the positions of even terms are given by A368998 (union of A345452 and 2*A358776) and A373375 (union of A345452 and 8*A345452), thus both are supersets of A345452.
%H Antti Karttunen, <a href="/A373367/b373367.txt">Table of n, a(n) for n = 1..100000</a>
%F a(n) = gcd(A373145(n), A373362(n)) = gcd(A373145(n), A373364(n)) = gcd(A373362(n), A373364(n)).
%o (PARI)
%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
%o A373367(n) = gcd([A001414(n), A003415(n), A276085(n)]);
%Y Cf. A001414, A003415, A276085, A345452 (gives the positions of even terms).
%Y Greatest common divisor of any two of these three: A373145, A373362, A373364.
%K nonn
%O 1,4
%A _Antti Karttunen_, Jun 03 2024
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