A297841 - OEIS

%I #22 Jan 13 2025 01:31:43

%S 1,8,18,36,50,90,98,160,171,250,242,392,338,490,500,656,578,882,722,

%T 1050,980,1210,1058,1640,1275,1690,1620,2058,1682,2522,1922,2688,2420,

%U 2890,2548,3726,2738,3610,3380,4328,3362,4900,3698,5082,4662,5290,4418,6688

%N a(n) = Sum_{d|n} max(d, n/d)^2.

%H Seiichi Manyama, <a href="/A297841/b297841.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 2*A001157(n) - A297792(n).

%F Sum_{k=1..n} a(k) ~ (2*zeta(3)/3) * n^3. - _Amiram Eldar_, Jan 12 2025

%p f:= n -> add(max(d,n/d)^2, d = numtheory:-divisors(n)):

%p map(f, [$1..100]); # _Robert Israel_, Jan 10 2018

%t f[n_] := Block[{d = Divisors@ n}, Plus @@ (Max[#, n/#]^2 & /@ d)]; Array[f, 50] (* _Robert G. Wilson v_, Jan 07 2018 *)

%o (PARI) {a(n) = sumdiv(n, d, max(d, n/d)^2)}

%Y Sum_{d|n} max(d, n/d)^k: A117003 (k=1), this sequence (k=2), A297842 (k=3), A297843 (k=4), A297844 (k=5).

%Y Cf. A001157, A002117, A297792.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 07 2018