A364171 - OEIS

%I #63 Jul 28 2023 15:52:48

%S 6,21,40,105,126,301,456,657,910,1221,1596,2041,2562,3165,3856,4641,

%T 5526,6517,7620,8841,10186,11661,13272,15025,16926,18981,21196,23577,

%U 26130,28861,31776,34881,38182,41685,45396,49321,53466,57837,62440,67281,72366,77701

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

%C Each term is a representative of the class of numbers with quotient n.

%C A364169 is the smallest m = b*c without requiring an increasing sequence. Sometimes the present sequence is still that minimum, a(n) = A364169(n).

%C Also subsequence of A364202.

%C Is a(n) = A062158(n+1) + 1 for n >= 6? - _Hugo Pfoertner_, Jul 23 2023

%e 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.

%t 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 *)

%Y Cf. A062158, A364169, A364202.

%K nonn

%O 1,1

%A _Jose Aranda_, Jul 12 2023

%E More terms from _Amiram Eldar_, Jul 12 2023