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A105327 Numbers n such that pi(n)=pi(d_1!)+pi(d_2!)+...+pi(d_k!) where d_1 d_2 ...d_k is the decimal expansion of n. 1

%I #7 Jan 11 2013 16:28:28

%S 0,1,2,115,1626,5370,5371,5570,5571,6170,6171,40854,373369,373469,

%T 419386,419658,419685,889609,889619

%N Numbers n such that pi(n)=pi(d_1!)+pi(d_2!)+...+pi(d_k!) where d_1 d_2 ...d_k is the decimal expansion of n.

%C There is no further term (the proof is easy).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Factorial.html">Factorial</a>.

%e 889619 is in the sequence because pi(889619)=pi(8!)+pi(8!)+pi(9!)+pi(6!)+pi(1!)+pi(9!).

%t Do[h = IntegerDigits[m]; l = Length[h]; If[PrimePi[m] == Sum[PrimePi[h[[k]]! ], {k, l}], Print[m]], {m, 0, 3000000}]

%Y Cf. A066457, A105328.

%K base,fini,full,nonn

%O 1,3

%A _Farideh Firoozbakht_, Apr 20 2005

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