A045977 Smallest number with same number of divisors as n!.

1, 1, 2, 6, 24, 120, 720, 5040, 27720, 166320, 1940400, 25225200, 230630400, 3920716800, 16295479200, 97772875200, 321253732800, 9316358251200, 767582252236800, 20724720810393600, 303962571885772800, 2861985254768640000, 1212989844306240000, 44880624239330880000

Offset

0,3

References

Don McDonald to sci.math, Mar 20 1999.

Links

Matthew House, Table of n, a(n) for n = 0..609

Matthew House, Python program

Formula

a(n) = A005179(A027423(n)). - R. J. Mathar, Aug 13 2012

Example

8!=40320 has 96 divisors, but 27720 is smaller with also 96 divisors. 9!=362880 has 160 divisors, but 166320 is smaller.

Prog

(PARI) a(n) = {nd = numdiv(n!); k = 1; while(numdiv(k) != nd, k++); k; } \\ Michel Marcus, Aug 28 2013

Crossrefs

Cf. A027423.

Sequence in context: A364427 A273694 A138113 * A177278 A173847 A154655

Adjacent sequences: A045974 A045975 A045976 * A045978 A045979 A045980

Keyword

nonn,nice

Author

Donald S. McDonald, Mar 20 1999

Extensions

More terms from David W. Wilson

a(21)-a(23) from Matthew House, Aug 14 2024

Status

approved