A066457 Numbers n such that product of factorials of digits of n equals pi(n) (A000720).

13, 1512, 1520, 1521, 12016, 12035, 226130351, 209210612202, 209210612212, 209210612220, 209210612221, 13030323000581525

Offset

1,1

Comments

The Caldwell/Honaker paper does not discuss this, only suggests further areas of investigation.

There are no other members of the sequence up to and including n=1000000. - Harvey P. Dale, Jan 07 2002

If 10n is in the sequence and 10n+1 is composite then 10n+1 is also in the sequence (the proof is easy). - Farideh Firoozbakht, Oct 24 2008

a(13) > 10^19 if it exists. - Chai Wah Wu, May 03 2018

Links

Table of n, a(n) for n=1..12.

C. Caldwell and G. L. Honaker, Jr., Is pi(6521)=6!+5!+2!+1! unique?

A discussion about this topic: bbs.emath.ac.cn [From Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008]

Example

a(5)=12016 because there are exactly 1!*2!*0!*1!*6! (or 1440) prime numbers less than or equal to 12016.
pi(209210612202) = 8360755200 = 2!*0!*9!*2!*1!*0!*6!*1!*2!*2!*0!*2!. [Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008]

Mathematica

Select[Range[1000000], Times@@( # !&/@IntegerDigits[ # ])==PrimePi[ # ]&]

Prog

(PARI) isok(n) = my(d = digits(n)); prod(k=1, #d, d[k]!) == primepi(n); \\ Michel Marcus, May 04 2018

Crossrefs

Cf. A000720, A066459, A049529, A105327.

Sequence in context: A220551 A185073 A185193 * A203515 A166929 A079917

Adjacent sequences: A066454 A066455 A066456 * A066458 A066459 A066460

Keyword

base,nonn

Author

Jason Earls, Jan 02 2002

Extensions

a(7) from Farideh Firoozbakht, Apr 20 2005

a(8)-a(11) from Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008

a(12) from Chai Wah Wu, May 03 2018

Status

approved