A251619 -id:A251619 - cp's OEIS frontend

A251715 Array: A251637(n,k) / prime(n).

1, 1, 2, 3, 3, 4, 2, 1, 5, 7, 2, 5, 5, 2, 3, 3, 1, 1, 7, 4, 6, 3, 1, 3, 3, 2, 7, 8, 2, 1, 2, 5, 4, 4, 9, 5, 3, 1, 5, 5, 4, 13, 9, 13, 10, 3, 1, 5, 2, 7, 9, 7, 17, 11, 11, 2, 1, 5, 3, 4, 4, 7, 9, 11, 15, 13, 2, 1, 2, 2, 7, 7, 9, 6, 6, 13, 17, 14, 3, 1, 3, 5

Offset: 1

Reinhard Zumkeller, Dec 09 2014

T(n,k) = A251637(n,k) / A000040(n);
A251637(n,k) = T(n,k) * A000040(n);
for n > 2: T(n,1) = A251619(n);
conjecture: A098550 is a permutation of the positive integers iff all rows are permutations of the positive integers.
For third column with row numbers > 4: see A251542. - Reinhard Zumkeller, Dec 16 2014

			.   n   p |  A251637(n,k) / p, with p = prime(n), n = 1..25, k = 1..20
.  -------+-----------------------------------------------------------
.   1   2 |  1 2 4 7 3  6 8  5 10 11 13 14 16  9 12 17 18 15 19 21 22
.   2   3 |  1 3 5 2 4  7 9 13 11 15 17  6  8 12 10 21 14 19 23 16 25
.   3   5 |  3 1 5 7 2  4 9 17 11 13  6 19  8 10 23 15 12 35 21 14 16
.   4   7 |  2 5 1 3 4 13 7  9  6  8 11 17 19 23 25 15 10 12 47 29 21
.   5  11 |  2 1 3 5 4  9 7  6  8 15 13 11 17 10 12 21 19 14 16 25 18
.   6  13 |  3 1 2 5 7  4 9  6  8 15 11 10 12 17 13 19 21 14 16 23 25
.   7  17 |  3 1 5 2 4  7 9  6 11  8 10 15 13 12 14 21 17 16 19 23 25
.   8  19 |  2 1 5 3 7  4 9  6  8 11 13 10 15 12 14 21 17 19 23 16 25
.   9  23 |  3 1 5 2 7  4 6  9  8 11 13 15 10 12 19 17 14 21 16 25 18
.  10  29 |  3 1 2 5 7  4 6  9  8 11 13 10 15 12 17 14 21 19 16 25 23
.  11  31 |  2 1 3 5 4  7 9  6 11 13  8 15 10 12 17 19 14 21 16 23 18
.  12  37 |  2 1 3 5 4  7 6  9  8 11 15 10 17 13 12 23 19 21 14 16 18
.  13  41 |  3 1 2 5 4  7 6  9 11  8 10 13 15 12 17 14 21 19 16 25 23
.  14  43 |  2 1 3 5 4  7 9  6 11  8 10 15 13 12 14 19 17 21 16 23 18
.  15  47 |  2 1 7 3 5  4 6  9 11  8 10 13 15 12 17 19 14 21 16 23 25
.  16  53 |  2 1 5 3 4  7 6  9  8 11 13 10 15 12 17 14 21 19 16 18 25
.  17  59 |  2 1 3 5 4  7 6  9 11  8 13 10 15 17 12 14 19 21 16 23 18
.  18  61 |  2 1 7 3 5  4 6  9 11  8 13 10 15 12 17 14 19 21 16 23 18
.  19  67 |  3 1 5 2 4  7 9  6  8 11 13 10 15 12 17 14 19 21 16 23 18
.  20  71 |  2 1 3 5 4  7 6  9  8 11 10 15 13 12 17 14 19 21 16 23 18
.  21  73 |  2 1 5 3 4  7 6  9  8 11 10 13 15 12 17 14 19 21 16 23 18
.  22  79 |  2 1 3 5 4  7 6  9  8 11 13 10 15 12 14 17 19 21 16 23 18
.  23  83 |  3 1 7 2 5  4 6  9 11  8 13 10 15 12 17 19 14 21 16 23 18
.  24  89 |  2 1 3 5 4  7 6  9  8 11 13 10 15 12 17 14 21 19 16 23 18
.  25  97 |  3 1 7 2 5  4 6  9 11  8 10 13 15 12 17 14 19 21 16 23 18 .
.  --------------------------------------------------------------------
See table A251637 for T(n,k) * p.

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Cf. A098550, A251637, A000040, A251619.

Wrong data replaced; Reinhard Zumkeller, Dec 15 2014

A251618 Smallest term in A098550 having prime(n) as a factor.

Original entry on oeis.org

2, 3, 15, 14, 22, 39, 51, 38, 69, 87, 62, 74, 123, 86, 94, 106, 118, 122, 201, 142, 146, 158, 249, 178, 291, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 514

Offset: 1

Reinhard Zumkeller, Dec 07 2014

nonn

Largest prime factor of a(n) = prime(n);
a(n) is composite for n > 2;
first column in A251637;
conjecture: for n > 2: a(n) = 2*prime(n) or a(n) = 3*prime(n);
conjecture: for n > 25: a(n) = 2*prime(n).

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A098550, A000040, A251637, A251619 (smallest prime factor), A006530.

import Data.List (find); import Data.Maybe (fromJust)
a251618 n = fromJust $
            find (\x -> mod x (fromIntegral $ a000040 n) == 0) a098550_list

nmax = 100;
b[n_] := b[n] = If[n <= 4, n, For[k = 1, True, k++, If[FreeQ[Array[b, n-1], k] && GCD[k, b[n-1]] == 1 && GCD[k, b[n-2]] > 1, Return[k]]]];
A098550 = Array[b, 12*nmax]; (* If the message Missing[NotFound] appears, the coefficient 12 in 12*nmax should be increased. *)
a[n_] := SelectFirst[A098550, Divisible[#, Prime[n]]&];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Sep 27 2021 *)

cp's OEIS Frontend

A251715 Array: A251637(n,k) / prime(n).

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