

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, 13030323000581525
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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


LINKS

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



KEYWORD

base,nonn


AUTHOR



EXTENSIONS

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


STATUS

approved



