A110069 Numbers n such that n = (d_1 + d_2 + ... + d_k)*prime(d_1*d_2*...*d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

188217, 216925, 329319, 22146969, 236256594, 269226639788

Offset: 1

Author

Farideh Firoozbakht, Jul 17 2005

Keywords

• nonn
• base
• fini
• more

Comments

There is no further term up to 660000000.

This sequence is finite since (d_1+d_2+...+d_k)*prime(d_1*d_2*...*d_k) <= 9k * prime(9^k) << 9^k * k^2 << n. The bound can be made effective using the results of Dusart or others; for example, a(n) < 10^150. These can be improved with more work, but completing the sequence seems hard. - Charles R Greathouse IV, May 07 2011

a(7) > 7*10^14, if it exists. - Giovanni Resta, Jun 01 2020

If it exists, a(7) > 10^18. - Max Alekseyev, Jan 28 2024

Examples

			236256594 is in the sequence because 236256594 = (2 + 3 + 6 + 2 + 5 + 6 + 5 + 9 +4)*prime(2*3*6*2*5*6*5*9*4).
		

Crossrefs

Cf. A009994, A097640.

Programs

Mathematica

Do[h = IntegerDigits[m]; l = Length[h]; If[Min[h] > 0 && m == Sum[h[[k]], {k, l}]*(Prime[Product[h[[k]], {k, l}]]), Print[m]], {m, 655000000}]

Extensions

a(6) from Giovanni Resta, Jun 01 2020