A105328 -id:A105328 - cp's OEIS frontend

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

Farideh Firoozbakht, Apr 20 2005

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

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

Eric Weisstein's World of Mathematics, Factorial.

Cf. A066457, A105328.

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

A066458 Numbers n such that Sum_{d runs through digits of n} d^d = pi(n) (cf. A000720).

Original entry on oeis.org

12, 22, 132, 34543, 612415, 27236725, 27236752, 311162281, 311163138, 327361548, 9237866583, 17499331217, 17499551725, 36475999489, 36475999498

Offset: 1

Jason Earls, Jan 02 2002

Note that only two terms, namely 34543 & 17499331217 are primes. So we have: 34543=prime(3^3+4^4+5^5+4^4+3^3), 17499331217=prime(1^1+7^7+4^4+9^9+9^9+3^3+3^3+1^1+2^2+1^1+7^7) and there is no other such prime. - Farideh Firoozbakht, Sep 23 2005

			a(3)=132 because there are exactly 1^1+3^3+2^2 (or 32) prime numbers less than or equal to 132.

C. Caldwell and G. L. Honaker, Jr., Is pi(6521)=6!+5!+2!+1! unique?

Cf. A105328, A105329.

Do[ If[ Apply[Plus, IntegerDigits[n]^IntegerDigits[n]] == PrimePi[n], Print[n]], {n, 1, 10^7} ]

More terms from Robert G. Wilson v, Jan 15 2002
Terms 27236725 onwards from Farideh Firoozbakht, Apr 21 2005 and Sep 17 2005
Sequence completed by Farideh Firoozbakht, Sep 23 2005

cp's OEIS Frontend

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.

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