A112718 Numbers m such that pi(m) = 1^d_1 + 2^d_2 + ... + k^d_k where d_1 d_2 ... d_k is the decimal expansion of m.

2, 12, 23, 113, 151, 5924, 14254, 106545, 1915765, 2798136, 31749441, 35282317, 35389065, 35389165, 105227821, 141291863, 193789064, 326730783, 839512048, 882012907, 884676937, 2780026914, 2997751947, 8493184690, 8493955191

Offset: 1

Author

Farideh Firoozbakht, Sep 17 2005

Keywords

• base
• fini
• full
• nonn

Comments

The largest term is less than 10^12 because if m>12 then 1^9+2^9+...+n^9 < pi(10^(m-1)). There is no further term up to 41*10^7.

Examples

			326730783 is in the sequence because pi(326730783) = 1^3 + 2^2 + 3^6 + 4^7 + 5^3 + 6^0 + 7^7 + 8^8 + 9^3 = 17618732.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..33 (full sequence)

Crossrefs

Cf. A000720, A035138, A112719, A112720.

Programs

Mathematica

Do[d=IntegerDigits[n];k=Length[d];If[PrimePi[n]==Sum[j^d[[j]], {j, k}], Print[n]], {n, 410000000}]

Extensions

a(19)-a(25) from Donovan Johnson, Nov 09 2010