A392093 a(n) is the terminal value obtained by repeatedly replacing the sorted set of positive divisors of n with the sorted set of consecutive differences, continuing until only one number remains.

1, 1, 2, 1, 4, 2, 6, 1, 4, 2, 10, 3, 12, 2, 8, 1, 16, 4, 18, 2, 8, 6, 22, 5, 16, 8, 8, 3, 28, 7, 30, 1, 8, 12, 22, 7, 36, 14, 8, 3, 40, 8, 42, 1, 22, 18, 46, 9, 36, 8, 8, 3, 52, 8, 36, 2, 8, 24, 58, 11, 60, 26, 16, 1, 40, 12, 66, 2, 8, 10, 70, 14, 72, 32, 32, 3

Offset

1,3

Comments

At each step, the differences are re-sorted and used exactly once, so the remaining number is strictly smaller while staying positive. The number of steps is <= tau(n) - 1 = A032741(n).

Links

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

Formula

A258409(n) <= a(n) < n for n > 1.

a(p) = A258409(p) = p - 1 for primes p (after one step).

a(2^k) = 1 for nonnegative integers k (after k steps).

a(k) = 1 => k is even or 1.

Example

a(6) = 2: {1, 2, 3, 6} -> {1, 3} -> {2}.
a(8) = 1: {1, 2, 4, 8} -> {1, 2, 4} -> {1, 2} -> {1}.
a(14) = 2: {1, 2, 7, 14} -> {1, 5, 7} -> {2, 4} -> {2}.

Maple

A392093 := proc(n) local d, i; d := NumberTheory:-Divisors(n); while 1 < nops(d) do d := {op(sort([seq(d[i + 1] - d[i], i = 1 .. nops(d) - 1)]))}; end do; op(d); end proc: seq(A392093(n), n = 1 .. 76);

Mathematica

A392093[n_] := First[NestWhile[Union[Differences[#]] &, Divisors[n], Length[#] > 1 &]];
Array[A392093, 100] (* Paolo Xausa, Jan 20 2026 *)

Crossrefs

Cf. A000005, A027750, A032741, A187202, A258409, A392079, A392080, A392094.

Sequence in context: A046791 A187203 A187202 * A345046 A125131 A003958

Adjacent sequences: A392090 A392091 A392092 * A392094 A392095 A392096

Keyword

nonn,easy

Author

Felix Huber, Jan 16 2026

Status

approved