A318459 -id:A318459 - cp's OEIS frontend

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

David W. Wilson

nonn

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

Antti Karttunen, Table of n, a(n) for n = 1..65537 (terms 1..1000 from T. D. Noe)

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).

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

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

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

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

A074389 a(n) = gcd(n, sigma(n), phi(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 6, 1, 4, 3, 2, 1, 4, 1, 1, 1, 2, 1, 6, 1, 8, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 6, 1, 4, 1, 2, 1, 4, 1, 1, 3, 1, 1, 2, 1, 2, 3

Offset: 1

Labos Elemer, Aug 23 2002

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000010, A000203, A073815, A050399, A009194, A009195, A009223, A074465, A074466.

In the old definition the erroneously given formula gcd(n, A000005(n), A000010(n)) is now sequence A318459. - Antti Karttunen, Sep 07 2018

Table[Apply[GCD, {w, DivisorSigma[1, w], EulerPhi[w]}], {w, 1, 128}]

A074389(n) = gcd([n, sigma(n), eulerphi(n)]); \\ Antti Karttunen, Sep 07 2018

a(n) = gcd(n, A000010(n), A000203(n)).

a(n) = gcd(n, A009223(n)). - Antti Karttunen, Sep 07 2018

Name corrected by Antti Karttunen, Sep 07 2018

A009213 a(n) = gcd(d(n), phi(n)), where d is the number of divisors of n (A000005) and phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 2, 4, 3, 4, 2, 2, 2, 2, 4, 1, 2, 6, 2, 2, 4, 2, 2, 8, 1, 4, 2, 6, 2, 8, 2, 2, 4, 4, 4, 3, 2, 2, 4, 8, 2, 4, 2, 2, 6, 2, 2, 2, 3, 2, 4, 6, 2, 2, 4, 8, 4, 4, 2, 4, 2, 2, 6, 1, 4, 4, 2, 2, 4, 8, 2, 12, 2, 4, 2, 6, 4, 8, 2, 2, 1, 4, 2, 12, 4, 2, 4, 8, 2, 12, 4, 2, 4, 2, 4, 4, 2, 6, 6, 1, 2, 8, 2, 8, 8

Offset: 1

David W. Wilson

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000005, A000010,

Cf. also A009191, A009195, A009223, A318459.

Table[GCD[DivisorSigma[0,n],EulerPhi[n]],{n,110}] (* Harvey P. Dale, May 12 2025 *)

A009213(n) = gcd(numdiv(n), eulerphi(n)); \\ Antti Karttunen, Sep 07 2018

cp's OEIS Frontend

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

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A074389 a(n) = gcd(n, sigma(n), phi(n)).

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A009213 a(n) = gcd(d(n), phi(n)), where d is the number of divisors of n (A000005) and phi is Euler's totient function (A000010).

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