|
|
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.
|
|
1
|
|
|
|
OFFSET
|
1,1
|
|
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
|
|
LINKS
|
|
|
EXAMPLE
|
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).
|
|
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}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,fini,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|