A352742 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.

2, 81, 512, 2401, 11101212, 34012224, 612220032, 20047612231936, 3904305912313344, 7800803212802061312, 1025300207121086650406, 213780015477322248820322, 14076019706120526112710656, 2670419511272061205254504361, 2759031540715333904109053133443, 10530400808911150200350000010411

Offset: 1

Author

Nicolas Bělohoubek, Mar 31 2022

Keywords

• nonn
• base

Comments

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

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

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

Conjecture: No term is a multiple of 5.

a(28) = 265^28, disproving the above conjecture. - Charles R Greathouse IV, Apr 02 2022

Examples

			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.
		

Crossrefs

Cf. A072408.

Extensions

a(7)-a(8) confirmed by Jon E. Schoenfield, Mar 31 2022

a(9)-a(16) from Charles R Greathouse IV, Apr 02 2022