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.

0, 1, 2, 115, 1626, 5370, 5371, 5570, 5571, 6170, 6171, 40854, 373369, 373469, 419386, 419658, 419685, 889609, 889619

Offset: 1

Author

Farideh Firoozbakht, Apr 20 2005

Keywords

• base
• fini
• full
• nonn

Comments

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

Examples

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

Links

• Eric Weisstein's World of Mathematics, Factorial.

Crossrefs

Cf. A066457, A105328.

Programs

Mathematica

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