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.

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..42.

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A062158, A364169, A364202.

Sequence in context: A225150 A056237 A364169 * A199194 A268223 A048036

Adjacent sequences: A364168 A364169 A364170 * A364172 A364173 A364174

Keyword

nonn

Author

Jose Aranda, Jul 12 2023

Extensions

More terms from Amiram Eldar, Jul 12 2023

Status

approved