A125168 -id:A125168 - 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

A280946 Numbers n such that n and number of proper divisors (A032741) of n are relatively prime and n is a nonprime (A018252).

Original entry on oeis.org

1, 8, 9, 10, 12, 14, 18, 22, 24, 25, 26, 28, 30, 32, 34, 35, 38, 40, 44, 46, 49, 52, 54, 55, 58, 60, 62, 63, 65, 66, 68, 72, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 90, 91, 92, 94, 95, 96, 98, 99, 102, 104, 106, 108, 110, 112, 114, 115, 116, 117, 118, 119, 121, 122, 124, 125, 126, 128, 130, 133, 134, 135, 136, 138

Offset: 1

Ilya Gutkovskiy, Jan 11 2017

Numbers n such that A125168(n) = 1 and A010051(n) = 0.

Numbers n such that gcd(n,A032741(n)) = 1 and A000005(n) != 2.

			12 is in the sequence because 12 is a nonprime, 12 has 5 proper divisors {1, 2, 3, 4, 6} and gcd(12,5) = 1.

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Cf. A000005, A003624, A010051, A014567, A032741, A046642, A125168.

Select[Range[139], CoprimeQ[#1, DivisorSigma[0, #1] - 1] && !PrimeQ[#1] & ]
Select[Range[139], GCD[#1, DivisorSigma[0, #1] - 1] == 1 && DivisorSigma[0, #1] != 2 &]

isok(n) = gcd(n, numdiv(n)-1) == 1; \\ Michel Marcus, Jan 14 2017

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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