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Largest m such that 1, 2, ..., m divide n^2.
5

%I #37 Mar 07 2016 02:38:51

%S 1,2,1,2,1,4,1,2,1,2,1,4,1,2,1,2,1,4,1,2,1,2,1,4,1,2,1,2,1,6,1,2,1,2,

%T 1,4,1,2,1,2,1,4,1,2,1,2,1,4,1,2,1,2,1,4,1,2,1,2,1,6,1,2,1,2,1,4,1,2,

%U 1,2,1,4,1,2,1,2,1,4,1,2,1,2,1,4,1,2,1

%N Largest m such that 1, 2, ..., m divide n^2.

%C Note that a(n) is equal to A071222(n-1) = A053669(n)-1 for the first 209 values of n. The first difference occurs at n=210, where a(210)=7, while A071222(209)=10. A235921 lists all n where a(n) differs from A071222(n-1). (Note also that a(n) is equal to A071222(n+29) for n=1..179.) - [Comment revised by _Antti Karttunen_, Jan 26 2014 because of the changed definition of A235921 and newly inserted a(0)=1 term of A071222.]

%C See A055874 for a similar comment concerning the difference between A055874 and A232098.

%C Average value is 1.9124064... = sum_{n>=1} 1/A019554(A003418(n)). - _Charles R Greathouse IV_, Jan 24 2014

%H Charles R Greathouse IV, <a href="/A235918/b235918.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A055874(n^2).

%F a(n) = A236454(n)-1.

%t a[n_] := Module[{m = 1}, While[Divisible[n^2, m++]]; m - 2]; Array[a, 100] (* _Jean-François Alcover_, Mar 07 2016 *)

%o (PARI) a(n) = my(m = 1); while ((n^2 % m) == 0, m++); m - 1; \\ _Michel Marcus_, Jan 17 2014

%Y One less than A236454.

%Y Cf. also A055874, A053669, A055926, A071222, A232098, A235921.

%K nonn

%O 1,2

%A _Michel Marcus_, Jan 17 2014