A235918 Largest m such that 1, 2, ..., m divide n^2.

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, 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, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1

Offset: 1

Author

Michel Marcus, Jan 17 2014

Keywords

• nonn

Comments

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.]

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

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

One less than A236454.

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

Programs

Mathematica

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

PARI

a(n) = my(m = 1); while ((n^2 % m) == 0, m++); m - 1; \\ Michel Marcus, Jan 17 2014

Formula

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

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