A009191 a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005).

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

Offset: 1

Author

David W. Wilson

Keywords

• nonn

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)

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).

Programs

Haskell

a009191 n = gcd n $ a000005 n
-- Reinhard Zumkeller, May 09 2013, Aug 14 2011

Mathematica

f[n_] := GCD[n, DivisorSigma[0, n]]; Array[f, 105] (* Robert G. Wilson v, Mar 27 2013 *)

PARI

a(n)=gcd(numdiv(n),n) \\ Charles R Greathouse IV, Mar 26 2013

Formula

a(n) = gcd(n, A000005(n)) = gcd(n, A049820(n)). - Antti Karttunen, Sep 25 2018