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

1,3

Comments

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

Links

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, Factorial.

Example

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

Mathematica

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

Crossrefs

Cf. A066457, A105328.

Sequence in context: A209184 A356724 A065670 * A260334 A357386 A257939

Adjacent sequences: A105324 A105325 A105326 * A105328 A105329 A105330

Keyword

base,fini,full,nonn

Author

Farideh Firoozbakht, Apr 20 2005

Status

approved