A392080 a(n) is the number of repeated difference values among the consecutive divisors of A259366(n).

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, 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, 2, 4, 2, 2, 1, 3, 1, 3, 1, 2, 2, 2, 2, 1, 4, 3, 2, 2, 3, 1

Offset

1,4

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Formula

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

Example

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.

Maple

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);

Mathematica

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

Crossrefs

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

Sequence in context: A269252 A291150 A292375 * A361702 A295218 A338430

Adjacent sequences: A392077 A392078 A392079 * A392081 A392082 A392083

Keyword

nonn

Author

Felix Huber, Jan 09 2026

Status

approved