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 A009191 a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005). 18
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(A046642(n)) = 1. 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 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 (terms 1..1000 from T. D. Noe) FORMULA a(n) = gcd(n, A000005(n)) = gcd(n, A049820(n)). - Antti Karttunen, Sep 25 2018 MATHEMATICA f[n_] := GCD[n, DivisorSigma[0, n]]; Array[f, 105] (* Robert G. Wilson v, Mar 27 2013 *) PROG (Haskell) a009191 n = gcd n \$ a000005 n -- Reinhard Zumkeller, May 09 2013, Aug 14 2011 (PARI) a(n)=gcd(numdiv(n), n) \\ Charles R Greathouse IV, Mar 26 2013 CROSSREFS Cf. A000005, A009194, A009195, A009205, A009213, A009230, A049820, A125168, A138010, A286540, A303781, A318459, A319337. Cf. A046642 (positions of ones). Sequence in context: A051119 A159269 A186728 * A229969 A260909 A114717 Adjacent sequences:  A009188 A009189 A009190 * A009192 A009193 A009194 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 22 10:32 EST 2019. Contains 319363 sequences. (Running on oeis4.)