A354998 - OEIS

%I #9 Jun 17 2022 18:11:45

%S 1,1,3,4,5,3,7,8,9,5,11,4,13,7,15,16,17,9,19,5,7,11,23,24,25,13,27,28,

%T 29,15,31,32,33,17,35,9,37,19,13,40,41,7,43,44,45,23,47,16,49,25,51,

%U 13,53,27,11,8,19,29,59,60,61,31,63,64,65,33,67,17,69,35,71,9,73,37,25,76,77,13,79,16,81,41,83,84

%N Smallest divisor d of n for which A344005(d) = A344005(n), where A344005(n) is the smallest positive integer m such that n divides m*(m+1).

%H Antti Karttunen, <a href="/A354998/b354998.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = n / A354999(n).

%t s[n_] := Module[{m = 1}, While[! Divisible[m*(m + 1), n], m++]; m]; a[n_] := Module[{sn = s[n], ds = Divisors[n]}, Do[If[s[d] == sn, Return[d]], {d, ds}]]; Array[a, 100] (* _Amiram Eldar_, Jun 17 2022 *)

%o (PARI)

%o A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005

%o A354998(n) = { my(x=A344005(n)); fordiv(n, d, if(A344005(d)==x, return(d))); };

%Y Cf. A344005, A354991, A354992, A354999.

%Y Cf. also A344758, A346088.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 17 2022