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%I #10 Jun 17 2022 18:11:53
%S 1,2,1,1,1,2,1,1,1,2,1,3,1,2,1,1,1,2,1,4,3,2,1,1,1,2,1,1,1,2,1,1,1,2,
%T 1,4,1,2,3,1,1,6,1,1,1,2,1,3,1,2,1,4,1,2,5,7,3,2,1,1,1,2,1,1,1,2,1,4,
%U 1,2,1,8,1,2,3,1,1,6,1,5,1,2,1,1,1,2,1,1,1,2,1,1,3,2,1,1,1,2,1,4,1,2,1,1,3
%N a(n) = n divided by the 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="/A354999/b354999.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = n / A354998(n).
%t 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[n/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 A354999(n) = { my(x=A344005(n)); fordiv(n, d, if(A344005(d)==x, return(n/d))); };
%Y Cf. A344005, A354991, A354992, A354994 (positions of 1's), A354998.
%Y Cf. also A344759, A346089.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jun 17 2022
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