A371728 - OEIS

%I #33 Jun 12 2024 17:41:55

%S 9,13,19,31,40,46,54,63,70,81,88,97,106,112,121,130,136,148,154,162,

%T 171,180,187,193,205,211,220,229,235,244,253,262,271,277,286,297,301,

%U 310,319,331,334,343,355,360,367,378,388,396,400,406,418,423,424,436,451,454,457,469,487,487,487,513,517,517

%N a(n) is the largest number that is the digit sum of an n-digit square number.

%C a(n) appears to be approximately equal to (33*n-11)/4.

%H Shouen Wang, <a href="https://bbs.emath.ac.cn/thread-19296-1-1.html">Chinese BBS: How many of these A's are there?</a>

%e a(6) = 46 because 46 is the largest digital sum encountered among all 6-digit squares (698896, 779689, 877969).

%t Array[Max@Map[Total@IntegerDigits[#^2] &, Range[Floor@Sqrt[10^(#)]], Floor@Sqrt[10^(# + 1) - 1]] &, 15]

%Y Cf. A004159, A067179, A348300, A348303, A370522.

%K nonn,base

%O 1,1

%A _Zhining Yang_, Apr 04 2024

%E a(22)-a(48) from _Zhao Hui Du_, Apr 05 2024

%E a(49)-a(62) from _Zhining Yang_, May 08 2024

%E a(63)-a(64) from _Zhining Yang_, May 23 2024