A067126 -id:A067126 - cp's OEIS frontend

A081998 Square array read by antidiagonals, alternating upwards and downwards: T(i, j) is the least number that is greater than the previous term and coprime to every number on the same row or column.

1, 2, 3, 4, 5, 7, 9, 11, 13, 17, 19, 21, 23, 26, 29, 31, 37, 41, 43, 47, 49, 53, 59, 60, 61, 63, 67, 71, 73, 79, 83, 88, 89, 97, 101, 103, 107, 109, 113, 115, 127, 131, 137, 139, 143, 149, 151, 155, 157, 161, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 198, 199

Offset: 0

Amarnath Murthy, Apr 05 2003

Is the sequence related to A067126? This should exhibit some number-theoretic properties.

			Array begins:
   1,  2,  7,  9, ...
   3,  5, 11, ...
   4, 13, ...
  17, ...
  ...

Charlie Neder, Table of n, a(n) for n = 0..10010

Cf. A081999, A082000, A082001.

More terms from David Wasserman, Jul 28 2004

A193339 Indices of record values in A001783.

Original entry on oeis.org

1, 3, 4, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

Offset: 1

M. F. Hasler, Jul 23 2011

nonn

Indices k such that A001783(k) is larger than all preceding terms of that sequence. The corresponding values A001783(k) are given in A193338.
It appears that, except for 1, 2, 4, and 9, this is all and only the primes. (It certainly includes all odd primes.) - Franklin T. Adams-Watters, Aug 11 2011
It appears that this is the sequence of indices of records in A206369. - Michel Marcus, Nov 04 2017

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A067126.

Block[{s = Table[Times @@ Select[Range@ n, CoprimeQ[n, #] &], {n, 250}], t}, t = Union@ FoldList[Max, s]; Map[FirstPosition[s, #][[1]] &, t]] (* or *)
Union[Prime@ Range[2, 53], Range[3]^2] (* Michael De Vlieger, Nov 04 2017 *)

m=0;for(n=1,599,m+0<(m=max(m,A001783(n))) & print1(n", "))

A067127 Composite numbers for which phi(n) >= phi(k) for all composite k from 1 to n-1.

Original entry on oeis.org

4, 6, 8, 9, 14, 15, 16, 20, 21, 25, 33, 35, 39, 45, 49, 65, 77, 85, 91, 95, 111, 115, 119, 121, 143, 155, 161, 169, 187, 203, 209, 217, 221, 247, 253, 287, 289, 319, 323, 341, 361, 391, 403, 407, 427, 437, 451, 473, 481, 493, 517, 527, 529, 583, 589, 611, 629

Offset: 1

Amarnath Murthy, Jan 09 2002

			33 is a member as phi(33)=20 which is >= the maximum phi value for composite numbers less than 33, namely phi(25)=20.

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Cf. A067126, A131195.

lista(n)={my(L=List(), m=0); for(k=2, oo, if(!isprime(k), my(t=eulerphi(k)); if(t>=m, listput(L,k); m=t; if(#L>=n, return(Vec(L))))))} \\ Andrew Howroyd, Dec 10 2024

cp's OEIS Frontend

A081998 Square array read by antidiagonals, alternating upwards and downwards: T(i, j) is the least number that is greater than the previous term and coprime to every number on the same row or column.

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A193339 Indices of record values in A001783.

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Mathematica

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A067127 Composite numbers for which phi(n) >= phi(k) for all composite k from 1 to n-1.

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