A352742 - OEIS

%I #54 Apr 05 2022 21:12:15

%S 2,81,512,2401,11101212,34012224,612220032,20047612231936,

%T 3904305912313344,7800803212802061312,1025300207121086650406,

%U 213780015477322248820322,14076019706120526112710656,2670419511272061205254504361,2759031540715333904109053133443,10530400808911150200350000010411

%N a(n) is the smallest number > 1 that is not divisible by 10 but is divisible by the n-th power of the sum of its digits.

%C a(n+1) >= a(n).

%C When A072408(n) is not multiple of 10 then a(n) <= A072408(n).

%C a(n) = m * k^n where m is a positive integer and k is the sum of digits of a(n).

%C Conjecture: No term is a multiple of 5.

%C a(28) = 265^28, disproving the above conjecture. - _Charles R Greathouse IV_, Apr 02 2022

%e For n=5, 11101212 is not divisible by 10 but is divisible by the 5th power of the sum of its digits, that being (1+1+1+0+1+2+1+2)^5 = 9^5. There is no smaller such number.

%Y Cf. A072408.

%K nonn,base

%O 1,1

%A _Nicolas Bělohoubek_, Mar 31 2022

%E a(7)-a(8) confirmed by _Jon E. Schoenfield_, Mar 31 2022

%E a(9)-a(16) from _Charles R Greathouse IV_, Apr 02 2022