A199968 -id:A199968 - cp's OEIS frontend

A199970 a(n) = the smallest number m with the smallest non-divisor n such that 1

0, 3, 4, 6, 12, 0, 60, 420, 840, 0, 2520, 0, 27720, 0, 0, 360360, 720720, 0, 12252240, 0, 0, 0, 232792560, 0, 5354228880, 0, 26771144400, 0, 80313433200, 0, 2329089562800, 72201776446800, 0, 0, 0, 0, 144403552893600, 0, 0, 0, 5342931457063200, 0, 219060189739591200

Offset: 1

Jaroslav Krizek, Nov 26 2011

nonn

			a(7) = 60 because 60 is the smallest number such that numbers k < 7 divides 60 but number 7 is not divisor of 60.

Cf. A003418, A199968, A199969.

a[n_] := If[PrimePowerQ[n], If[n <= 3, n+1, LCM @@ Range[n-1]], 0]; Array[a, 50] (* Amiram Eldar, Aug 06 2024 *)

a(n) > 0 for prime powers n = p^k (p prime, k >= 1) else 0.

a(n) = A003418(n-1) for n = p^k > 3 (p prime, k >= 1). - Amiram Eldar, Aug 06 2024

More terms from Amiram Eldar, Aug 06 2024

A173540 Triangle read by rows in which row n lists the proper nondivisors of n, or zero if n <= 2.

Original entry on oeis.org

0, 0, 2, 3, 2, 3, 4, 4, 5, 2, 3, 4, 5, 6, 3, 5, 6, 7, 2, 4, 5, 6, 7, 8, 3, 4, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 7, 8, 9, 10, 11, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 2, 3, 4, 5, 6, 7

Offset: 1

Omar E. Pol, May 24 2010

Define "proper nondivisors of n" as the positive numbers less than n that do not divide n.
Note that a(1) = 0 and a(2) = 0, by convention.
Row sums give A024816.
Row products give A055067, except the first two rows. - Reinhard Zumkeller, Feb 06 2012
T(n,1) = A199968(n). - Reinhard Zumkeller, Oct 02 2015
The n-th row has A049820(n) terms. - Michel Marcus, Dec 23 2015

			If written as a triangle:
  0;
  0;
  2;
  3;
  2, 3, 4;
  4, 5;
  2, 3, 4, 5,  6;
  3, 5, 6, 7;
  2, 4, 5, 6,  7,  8;
  3, 4, 6, 7,  8,  9;
  2, 3, 4, 5,  6,  7,  8,  9, 10;
  5, 7, 8, 9, 10, 11;
  2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12;
  3, 4, 5, 6,  8,  9, 10, 11, 12, 13;
  2, 4, 6, 7,  8,  9, 10, 11, 12, 13, 14;
  3, 5, 6, 7,  9, 10, 11, 12, 13, 14, 15;

Reinhard Zumkeller, Rows n=1..150 of triangle, flattened

Cf. A027750, A049820, A177235.

Cf. A199968, A024816 (row sums).

a173540 n k = a173540_row n !! (k-1)
a173540_row n = a173540_tabf !! (n-1)
a173540_tabf = [0] : [0] : map
               (\v -> [w | w <- [2 .. v - 1], mod v w > 0]) [3..]
-- Reinhard Zumkeller, Oct 02 2015, Feb 06 2012

Join[{0, 0}, Flatten[Table[Complement[Range[n], Divisors[n]], {n, 1, 20}]]] (* Geoffrey Critzer, Dec 13 2014 *)

A199969 a(n) = the greatest non-divisor h of n (1 < h < n), or 0 if no such h exists.

Original entry on oeis.org

0, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset: 1

Jaroslav Krizek, Nov 26 2011

From Paul Curtz, Feb 09 2015: (Start)
The nonnegative numbers with 0 instead of 1. See A254667(n), which is linked to the Bernoulli numbers A164555(n)/A027642(n), an autosequence of the second kind.
Offset 0 could be chosen.
An autosequence of the second kind is a sequence whose main diagonal is the first upper diagonal multiplied by 2. If the first upper diagonal is
s0, s1, s2, s3, s4, s5, ...,
the sequence is
Ssk(n) = 2*s0, s0, s0 + 2*s1, s0 +3*s1, s0 + 4*s1 + 2*s2, s1 + 5*s1 + 5*s2, etc.
The corresponding coefficients are A034807(n), a companion to A011973(n).
The binomial transform of Ssk(n) is (-1)^n*Ssk(n).
Difference table of a(n):
   0,  0, 2, 3, 4, 5, 6, 7, ...
   0,  2, 1, 1, 1, 1, 1, ...
   2, -1, 0, 0, 0, 0 ...
  -3,  1, 0, 0, 0, ...
   4, -1, 0, 0, ...
  -5,  1, 0, ...
   6, -1, ...
   7, ...
  etc.
a(n) is an autosequence of the second kind. See A054977(n).
The corresponding autosequence of the first kind (a companion) is 0, 0 followed by the nonnegative numbers (A001477(n)). Not in the OEIS.
Ssk(n) = 2*Sfk(n+1) - Sfk(n) where Sfk(n) is the corresponding sequence of the first kind (see A254667(n)).
(End)
Number of binary sequences of length n-1 that contain exactly one 0 and at least one 1. - Enrique Navarrete, May 11 2021

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A199968 (the smallest non-divisor h of n (1A199970. A001477, A011973, A034807, A054977, A254667.
Cf. A007978.
Essentially the same as A000027, A028310, A087156 etc.

Join[{0,0},Table[Max[Complement[Range[n],Divisors[n]]],{n,3,70}]] (* or *) Join[{0,0},Range[2,70]] (* Harvey P. Dale, May 31 2014 *)

if(n>2,n-1,0) \\ Charles R Greathouse IV, Sep 02 2015

a(n) = n-1 for n >= 3.

E.g.f.: 1-x^2/2+(x-1)*exp(x). - Enrique Navarrete, May 11 2021

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A199970 a(n) = the smallest number m with the smallest non-divisor n such that 1

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A173540 Triangle read by rows in which row n lists the proper nondivisors of n, or zero if n <= 2.

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A199969 a(n) = the greatest non-divisor h of n (1 < h < n), or 0 if no such h exists.

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