A392080 - OEIS

%I #9 Jan 16 2026 10:01:24

%S 1,1,1,2,1,2,1,2,2,2,1,3,3,1,1,1,2,1,3,2,2,2,3,2,1,4,1,2,2,1,3,1,2,2,

%T 2,3,1,2,1,2,2,3,2,2,2,4,1,4,2,3,1,2,1,5,1,3,3,2,1,5,2,2,2,1,2,1,3,3,

%U 2,4,2,2,1,3,1,3,1,2,2,2,2,1,4,3,2,2,3,1

%N a(n) is the number of repeated difference values among the consecutive divisors of A259366(n).

%H Felix Huber, <a href="/A392080/b392080.txt">Table of n, a(n) for n = 1..10000</a>

%F 1 <= a(n) <= A000005(A259366(n)) - A060682(A259366(n)) - A392079(n) + 1.

%e The divisors of A259366(10) = 42 are {1, 2, 3, 6, 7, 14, 21, 42}. The consecutive differences are [1, 1, 3, 1, 7, 7, 21]. Among these, the values 1 and 7 occur more than once, so a(10) = 2.

%p A392080 := proc(n) local a, d, i, k, l; option remember; a := 0; if n = 1 then [6, 2]; else for k from A392080(n - 1)[1] + 1 do d := NumberTheory:-Divisors(k); l := [seq(d[i + 1] - d[i], i = 1 .. nops(d) - 1)]; a := nops(select(x -> 1 < x, [seq(numboccur(i, l), i = 1 .. max(l))])); if 0 < a then return [k, a]; end if; end do; end if; end proc: seq(A392080(n)[2], n = 1 .. 88);

%t Table[If[DuplicateFreeQ[#], Nothing, Count[Tally[#][[All, 2]], _?(#>1 &)]] & [Differences[Divisors[k]]], {k, 300}] (* _Paolo Xausa_, Jan 16 2026 *)

%Y Cf. A000005, A027750, A060682, A193829, A259366, A392079.

%K nonn

%O 1,4

%A _Felix Huber_, Jan 09 2026