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 A009191 a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005). 25
 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 Conjecture is true. See David A. Corneth's comment in A324553. - Antti Karttunen, Mar 06 2019 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, A322979, A322980, A323073. Cf. A046642 (positions of ones), A324553 (position of the first occurrence of each n). Sequence in context: A159269 A186728 A158298 * A229969 A260909 A114717 Adjacent sequences:  A009188 A009189 A009190 * A009192 A009193 A009194 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 26 16:58 EST 2020. Contains 331280 sequences. (Running on oeis4.)