A122377 -id:A122377 - cp's OEIS frontend

A124332 a(n) = ((n mod d(n)) +1)th divisor of n, where d(n) is number of positive divisors of n.

1, 1, 3, 2, 5, 3, 7, 1, 1, 5, 11, 1, 13, 7, 15, 2, 17, 1, 19, 4, 3, 11, 23, 1, 5, 13, 27, 14, 29, 15, 31, 4, 3, 17, 35, 1, 37, 19, 39, 1, 41, 3, 43, 4, 9, 23, 47, 24, 7, 5, 51, 26, 53, 27, 55, 1, 3, 29, 59, 1, 61, 31, 9, 2, 5, 3, 67, 4, 3, 35, 71, 1, 73, 37, 15, 38, 7, 39, 79, 1, 3, 41, 83, 1

Offset: 1

Leroy Quet and Ray Chandler, Oct 26 2006

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A000005, A122377, A124333.

f[n_] := Block[{d = Divisors[n]}, d[[Mod[n, Length[d]] + 1]]];Table[f[n], {n, 90}] (* Ray Chandler, Oct 26 2006 *)

A122383 a(n) = m-th positive integer which is coprime to n, where phi(n) is number of positive integers which are <= n and are coprime to n and m = phi(n) if phi(n)|n, else m = n mod phi(n).

Original entry on oeis.org

1, 1, 1, 3, 1, 5, 1, 7, 4, 3, 1, 11, 1, 3, 13, 15, 1, 17, 1, 9, 16, 3, 1, 23, 6, 3, 13, 9, 1, 19, 1, 31, 20, 3, 16, 35, 1, 3, 23, 19, 1, 19, 1, 7, 38, 3, 1, 47, 8, 23, 29, 7, 1, 53, 19, 17, 32, 3, 1, 43, 1, 3, 46, 63, 22, 19, 1, 7, 38, 61, 1, 71, 1, 3, 64, 7, 20, 19, 1, 39, 40, 3, 1, 41, 27, 3

Offset: 1

Leroy Quet, Oct 19 2006

nonn

Cf. A000010, A122377, A124333.

f[n_] := Block[{k = 0, m = Mod[n, EulerPhi[n], 1]},While[m > 0,k++;While[GCD[n, k] > 1, k++ ];m--;];k];Table[f[n], {n, 90}] (* Ray Chandler, Oct 26 2006 *)

Edited and extended by Ray Chandler, Oct 26 2006

A298734 a(n) = n-th term in periodic sequence repeating the divisors of n in decreasing order.

Original entry on oeis.org

1, 1, 3, 4, 5, 3, 7, 1, 1, 5, 11, 1, 13, 7, 3, 16, 17, 1, 19, 10, 21, 11, 23, 1, 25, 13, 3, 4, 29, 3, 31, 16, 33, 17, 5, 1, 37, 19, 3, 1, 41, 21, 43, 22, 9, 23, 47, 3, 49, 25, 3, 4, 53, 3, 5, 1, 57, 29, 59, 1, 61, 31, 9, 64, 65, 33, 67, 34, 69, 5, 71, 1, 73, 37, 15, 4, 77, 3, 79, 1, 81, 41, 83, 1, 85, 43, 3, 1, 89, 10, 7, 46, 93, 47

Offset: 1

Franklin T. Adams-Watters, Jan 25 2018

nonn

			The divisors of 6 are 1, 2, 3, 6, which reversed is 6,3,2,1; repeating that produces the sequence 6, 3, 2, 1, 6, 3, 2, 1, 6, 3, 2, 1, ...; the 6th term in that sequence is 3, so a(6) = 3.

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Cf. A122377 (n/a(n)), A033950 (indices of 1's).

with(numtheory):
a:= n-> n/(l-> l[1+irem(n-1, nops(l))])(sort([divisors(n)[]])):
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 29 2018

Table[PadRight[{},n,Reverse[Divisors[n]]][[-1]],{n,100}] (* Harvey P. Dale, Jul 21 2024 *)

a(n) = my(d=Vecrev(divisors(n))); if (n % #d, d[n % #d], 1); \\ Michel Marcus, Jan 26 2018

cp's OEIS Frontend

A124332 a(n) = ((n mod d(n)) +1)th divisor of n, where d(n) is number of positive divisors of n.

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A122383 a(n) = m-th positive integer which is coprime to n, where phi(n) is number of positive integers which are <= n and are coprime to n and m = phi(n) if phi(n)|n, else m = n mod phi(n).

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A298734 a(n) = n-th term in periodic sequence repeating the divisors of n in decreasing order.

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