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%I #40 Mar 31 2019 04:09:15
%S 1,2,1,1,1,2,1,4,3,2,1,6,1,2,1,1,1,6,1,2,1,2,1,8,1,2,1,2,1,2,1,2,1,2,
%T 1,9,1,2,1,8,1,2,1,2,3,2,1,2,1,2,1,2,1,2,1,8,1,2,1,12,1,2,3,1,1,2,1,2,
%U 1,2,1,12,1,2,3,2,1,2,1,10,1,2,1,12,1,2,1,8,1,6,1,2,1,2,1,12,1,2,3,1,1,2,1,8,1
%N a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005).
%C a(A046642(n)) = 1.
%C First occurrence of k: 1, 2, 9, 8, 400, 12, 3136, 24, 36, 80, 123904, 60, 692224, 448, 2025, 384, .... Conjecture: each k is present. - _Robert G. Wilson v_, Mar 27 2013
%C Conjecture is true. See _David A. Corneth_'s comment in A324553. - _Antti Karttunen_, Mar 06 2019
%H Antti Karttunen, <a href="/A009191/b009191.txt">Table of n, a(n) for n = 1..65537</a> (terms 1..1000 from T. D. Noe)
%F a(n) = gcd(n, A000005(n)) = gcd(n, A049820(n)). - _Antti Karttunen_, Sep 25 2018
%t f[n_] := GCD[n, DivisorSigma[0, n]]; Array[f, 105] (* _Robert G. Wilson v_, Mar 27 2013 *)
%o (Haskell)
%o a009191 n = gcd n $ a000005 n
%o -- _Reinhard Zumkeller_, May 09 2013, Aug 14 2011
%o (PARI) a(n)=gcd(numdiv(n),n) \\ _Charles R Greathouse IV_, Mar 26 2013
%Y Cf. A000005, A009194, A009195, A009205, A009213, A009230, A049820, A125168, A138010, A286540, A303781, A318459, A319337, A322979, A322980, A323073.
%Y Cf. A046642 (positions of ones), A324553 (position of the first occurrence of each n).
%K nonn
%O 1,2
%A _David W. Wilson_
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