A066150 Maximal number of divisors of any n-digit number.

4, 12, 32, 64, 128, 240, 448, 768, 1344, 2304, 4032, 6720, 10752, 17280, 26880, 41472, 64512, 103680, 161280, 245760, 368640, 552960, 860160, 1290240, 1966080, 2764800, 4128768, 6193152, 8957952, 13271040, 19660800, 28311552, 41287680, 59719680, 88473600, 127401984, 181665792, 264241152, 382205952, 530841600

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Formula

a(n) = largest integer m such that A005179(m) < 10^n. - Max Alekseyev, Apr 29 2010

a(n) = A000005(A066151(n)). - Amiram Eldar, Jul 02 2019

Example

a(1) = 4 since 8 has 4 divisors and that is the record for 1-digit numbers.

Prog

(PARI) a066150(m, n) = local(d, a, k, b); for(d=m, n, a=0; for(k=10^d, 10^(d+1)-1, b =numdiv(k); if(b>a, a=b)); print1(a, ", "))
a066150(0, 6)

Crossrefs

Cf. A000005, A066151, A069650,

Cf. A130130 (minimal number of divisors of any n-digit number). [Jaroslav Krizek, Jul 18 2010]

Sequence in context: A005104 A028921 A028922 * A233458 A335687 A348864

Adjacent sequences: A066147 A066148 A066149 * A066151 A066152 A066153

Keyword

nonn,base,easy

Author

Joseph L. Pe, Dec 12 2001

Extensions

One more term from Klaus Brockhaus, Dec 13 2001

Further terms from Vladeta Jovovic and Vladimir Baltic, Dec 16 2001

Extended further by David Wasserman, Jan 25 2002

Status

approved