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A066457 Numbers n such that product of factorials of digits of n equals pi(n) (A000720). 5


%S 13,1512,1520,1521,12016,12035,226130351,209210612202,209210612212,

%T 209210612220,209210612221,13030323000581525

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

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

%C There are no other members of the sequence up to and including n=1000000. - _Harvey P. Dale_, Jan 07 2002

%C 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

%C a(13) > 10^19 if it exists. - _Chai Wah Wu_, May 03 2018

%H C. Caldwell and G. L. Honaker, Jr., <a href="https://utm.edu/staff/caldwell/preprints/6521.pdf">Is pi(6521)=6!+5!+2!+1! unique?</a>

%H A discussion about this topic: <a href="http://bbs.emath.ac.cn/thread-918-1-1.html">bbs.emath.ac.cn</a> [From Qu,Shun Liang (medie2006(AT)126.com), Nov 23 2008]

%e a(5)=12016 because there are exactly 1!*2!*0!*1!*6! (or 1440) prime numbers less than or equal to 12016.

%e 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]

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

%o (PARI) isok(n) = my(d = digits(n)); prod(k=1, #d, d[k]!) == primepi(n); \\ _Michel Marcus_, May 04 2018

%Y Cf. A000720, A066459, A049529, A105327.

%K base,nonn

%O 1,1

%A _Jason Earls_, Jan 02 2002

%E a(7) from _Farideh Firoozbakht_, Apr 20 2005

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

%E a(12) from _Chai Wah Wu_, May 03 2018

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Last modified March 4 08:38 EST 2021. Contains 341781 sequences. (Running on oeis4.)