A263098 a(n) = Max( tau(k) : k=1,2,3,...,n^2 ) where tau(k) = A000005(k) is the number of divisors of k.

1, 3, 4, 6, 8, 9, 10, 12, 12, 12, 16, 16, 16, 18, 18, 20, 20, 20, 24, 24, 24, 24, 24, 24, 24, 24, 30, 30, 32, 32, 32, 32, 32, 32, 32, 36, 36, 36, 36, 36, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 72

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..2080

Formula

a(n) = A070319(A000290(n)).

Mathematica

Table[Max[DivisorSigma[0, #] & /@ Range[n^2]], {n, 101}] (* Michael De Vlieger, Oct 11 2015 *)

Prog

(PARI)
A070319(n, m=1, s=2)={for(k=s, n, m<numdiv(k)&m=numdiv(k)); m}; \\ This function from M. F. Hasler, Sep 12 2012
A263098 = n -> A070319(n^2); \\ Slow without memoization.
for(n=1, 2080, write("b263098.txt", n, " ", A263098(n)));
(Scheme) (define (A263098 n) (A070319 (A000290 n)))

Crossrefs

Cf. A000290, A070319, A262514.

Cf. A263096, A263097.

Sequence in context: A156167 A090864 A118300 * A317391 A134745 A183867

Adjacent sequences: A263095 A263096 A263097 * A263099 A263100 A263101

Keyword

nonn

Author

Antti Karttunen, Oct 10 2015

Status

approved