

A066457


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


5



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

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..11.
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! [From Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008]


MATHEMATICA

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


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

There are no other members of the sequence up to and including n=1000000.  Harvey P. Dale, Jan 07 2002
226130351 from Farideh Firoozbakht, Apr 20 2005
Four more terms from Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008


STATUS

approved



