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%I #31 Nov 08 2021 09:05:44
%S 16,53,63,364,437,545,573,829,963,5449,6475,23797,67458,2475998
%N Numbers m such that the product of the digits of m is equal to the number of primes less than m.
%C This sequence is finite with its largest term < 10^70. - _Stefan Steinerberger_, Apr 24 2006
%C a(15) > 1.288 * 10^10 if it exists. - _Kevin P. Thompson_, Oct 19 2021
%e 364 is in the sequence because the product of its digits is 3*6*4 = 72 and there are 72 prime numbers smaller than 364.
%t Select[Range[50000], DigitCount[ # ][[10]] == 0 && Product[i^DigitCount[ # ][[i]], {i, 1, 9}] == PrimePi[ # - 1] &] (* _Stefan Steinerberger_, Apr 24 2006 *)
%t g[n_] := Product[IntegerDigits[n][[m]], {m, 1, Length[IntegerDigits[n]]}]; Do[If[g[n] == PrimePi[n], Print[n]], {n, 1, 10000000}] (* Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006 *)
%o (PARI) isok(m) = vecprod(digits(m)) == primepi(m); \\ _Michel Marcus_, Oct 23 2021
%Y Cf. A000720, A007954, A097220.
%K nonn,base,fini,more
%O 1,1
%A Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006
%E More terms from _Zak Seidov_, _Stefan Steinerberger_ and Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006
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