cp's OEIS Frontend

A361255 Triangle read by rows: row n lists the exponential unitary divisors of n.

%I A361255 #17 May 30 2025 08:02:06
%S A361255 1,2,3,2,4,5,6,7,2,8,3,9,10,11,6,12,13,14,15,2,16,17,6,18,19,10,20,21,
%T A361255 22,23,6,24,5,25,26,3,27,14,28,29,30,31,2,32,33,34,35,6,12,18,36,37,
%U A361255 38,39,10,40,41,42,43,22,44,15,45,46,47,6,48,7,49,10,50,51,26,52,53,6,54,55,14,56,57,58,59
%N A361255 Triangle read by rows: row n lists the exponential unitary divisors of n.
%C A361255 Starts to differ from A322791 in row n=16, where 4 is an exponential divisor but not an exponential unitary divisor.
%H A361255 Amiram Eldar, <a href="/A361255/b361255.txt">Table of n, a(n) for n = 1..15331</a> (first 10000 rows, flattened)
%H A361255 Nicuşor Minculete and László Tóth, <a href="https://doi.org/10.71352/ac.35.205">Exponential unitary divisors</a>, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 35 (2011), pp. 205-216.
%p A361255 A361255 := proc(n)
%p A361255     local expundivs ,d,isue,p,ai,bi;
%p A361255     expudvs := {} ;
%p A361255     for d in numtheory[divisors](n) do
%p A361255         isue := true ;
%p A361255         for p in numtheory[factorset](n) do
%p A361255             ai := padic[ordp](n,p) ;
%p A361255             bi := padic[ordp](d,p) ;
%p A361255             if bi > 0 then
%p A361255                 if modp(ai,bi) <>0 or igcd(bi,ai/bi) <> 1 then
%p A361255                     isue := false;
%p A361255                 end if;
%p A361255             else
%p A361255                 isue := false ;
%p A361255             end if;
%p A361255         end do;
%p A361255         if isue then
%p A361255             expudvs := expudvs union {d} ;
%p A361255         end if;
%p A361255     end do:
%p A361255     sort(expudvs) ;
%p A361255 end proc:
%p A361255 seq(op(A361255(n)),n=1..60) ;
%t A361255 udivQ[n_, m_] := (n > 0 && m > 0 && Divisible[n, m] && CoprimeQ[m, n/m]);
%t A361255 expuDivQ[n_, d_] := Module[{f = FactorInteger[n]}, And @@ MapThread[udivQ, {f[[;; , 2]], IntegerExponent[d, f[[;; , 1]]]}]]; expuDivs[1] = {1};
%t A361255 expuDivs[n_] := Module[{d = Rest[Divisors[n]]}, Select[d, expuDivQ[n, #] &]];
%t A361255 Table[expuDivs[n], {n, 1, 70}] // Flatten (* _Amiram Eldar_, Mar 11 2023 *)
%Y A361255 Cf. A322857 (row sums), A278908 (row lengths), A322791 (includes non-unitary exp divs).
%K A361255 nonn,tabf
%O A361255 1,2
%A A361255 _R. J. Mathar_, Mar 06 2023