A062158 -id:A062158 - cp's OEIS frontend

A274602 Triangle read by rows: T(n,k) = k*(n-k+1)^2 + n - k, 0 <= k <= n.

0, 1, 1, 2, 5, 2, 3, 11, 9, 3, 4, 19, 20, 13, 4, 5, 29, 35, 29, 17, 5, 6, 41, 54, 51, 38, 21, 6, 7, 55, 77, 79, 67, 47, 25, 7, 8, 71, 104, 113, 104, 83, 56, 29, 8, 9, 89, 135, 153, 149, 129, 99, 65, 33, 9, 10, 109, 170, 199, 202, 185, 154, 115, 74, 37, 10

Offset: 1

Juri-Stepan Gerasimov, Dec 01 2016

Mirrored version of a(n) is T(n,k) = (n-k)*(k+1)^2+k, 0 <= k <= n, read by rows:
0
 1
 5   2
 9  11   3
13  20  19   4
17  29  35  29   5
As an infinite square array (matrix) with comments:
 1   2   3   4   5                      A001477
 5  11  19  29  41                      A028387
 9  20  35  54  77                      A014107
13  29  51  79 113                      A144391
17  38  67 104 149                      A182868
21  47  83 129 185

			0; 1,1; 2,5,2; 3,11,9,3; 4,19,20,13,4; 5,29,35,29,17,5; ...
As an infinite triangular array:
0
1   1
2   5   2
3  11   9    3
4  19  20   13    4
5  29  35   29   17    5
As an infinite square array (matrix) with comments:
0   1   2    3    4    5                   A001477
1   5   9   13   17   21                   A016813
2  11  20   29   38   47                   A017185
3  19  35   51   67   83
4  29  54   79  104  129
5  41  77  113  149  185

Cf. A002064, A001477, A016813, A017185, A062158 (central column). A028387, A014107, A144391, A182868.

Cf. Triangle read by rows: T(n,k) = k*(n-k+1)^m+n-k, 0 <= k <= n: A003056 (m = 0), A059036 (m = 1), A278910 (m = k).

/* As triangle */ [[k*(n-k+1)^2+n-k: k in [0..n]]: n in [0..10]];

Table[k (n - k + 1)^(k + #) + n - k &[2 - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Dec 02 2016 *)

A364171 a(n) = m is the least m = bc > a(n-1) such that (b+c)n = m-1 where 1 < b <= c < m.

Original entry on oeis.org

6, 21, 40, 105, 126, 301, 456, 657, 910, 1221, 1596, 2041, 2562, 3165, 3856, 4641, 5526, 6517, 7620, 8841, 10186, 11661, 13272, 15025, 16926, 18981, 21196, 23577, 26130, 28861, 31776, 34881, 38182, 41685, 45396, 49321, 53466, 57837, 62440, 67281, 72366, 77701

Offset: 1

Jose Aranda, Jul 12 2023

nonn

Each term is a representative of the class of numbers with quotient n.
A364169 is the smallest m = b*c without requiring an increasing sequence. Sometimes the present sequence is still that minimum, a(n) = A364169(n).
Also subsequence of A364202.
Is a(n) = A062158(n+1) + 1 for n >= 6? - Hugo Pfoertner, Jul 23 2023

			For n = 7, a(7) = 456 because it is the smallest number m > 301 = a(6) that has a pair of distinct proper divisors b = 8 and c = 57 that give b*c = 8*57 = 456 and (b+c)*n = (8 + 57)*7 = 456 - 1.

Cf. A062158, A364169, A364202.

f[kmin_, n_] := f[kmin, n] = Module[{k = kmin + 1}, While[PrimeQ[k] || !AnyTrue[Rest@ Divisors[k], #^2 <= k && k - 1 == (# + k/#)*n &], k++]; k]; Rest@ FoldList[f][Join[{5}, Range[50]]] (* Amiram Eldar, Jul 12 2023 *)

More terms from Amiram Eldar, Jul 12 2023

cp's OEIS Frontend

A274602 Triangle read by rows: T(n,k) = k*(n-k+1)^2 + n - k, 0 <= k <= n.

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A364171 a(n) = m is the least m = bc > a(n-1) such that (b+c)n = m-1 where 1 < b <= c < m.

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cp's OEIS Frontend

A274602 Triangle read by rows: T(n,k) = k*(n-k+1)^2 + n - k, 0 <= k <= n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Mathematica

A364171 a(n) = m is the least m = b*c > a(n-1) such that (b+c)*n = m-1 where 1 < b <= c < m.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A364171 a(n) = m is the least m = bc > a(n-1) such that (b+c)n = m-1 where 1 < b <= c < m.