A392093 - OEIS

%I #9 Jan 20 2026 20:11:19

%S 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,

%T 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,

%U 24,58,11,60,26,16,1,40,12,66,2,8,10,70,14,72,32,32,3

%N 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.

%C 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).

%H Felix Huber, <a href="/A392093/b392093.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

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

%e a(6) = 2: {1, 2, 3, 6} -> {1, 3} -> {2}.

%e a(8) = 1: {1, 2, 4, 8} -> {1, 2, 4} -> {1, 2} -> {1}.

%e a(14) = 2: {1, 2, 7, 14} -> {1, 5, 7} -> {2, 4} -> {2}.

%p 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);

%t A392093[n_] := First[NestWhile[Union[Differences[#]] &, Divisors[n], Length[#] > 1 &]];

%t Array[A392093, 100] (* _Paolo Xausa_, Jan 20 2026 *)

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

%K nonn,easy

%O 1,3

%A _Felix Huber_, Jan 16 2026