A297844 -id:A297844 - cp's OEIS frontend

A297841 a(n) = Sum_{d|n} max(d, n/d)^2.

1, 8, 18, 36, 50, 90, 98, 160, 171, 250, 242, 392, 338, 490, 500, 656, 578, 882, 722, 1050, 980, 1210, 1058, 1640, 1275, 1690, 1620, 2058, 1682, 2522, 1922, 2688, 2420, 2890, 2548, 3726, 2738, 3610, 3380, 4328, 3362, 4900, 3698, 5082, 4662, 5290, 4418, 6688

Offset: 1

Seiichi Manyama, Jan 07 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

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

Cf. A001157, A002117, A297792.

f:= n -> add(max(d,n/d)^2, d = numtheory:-divisors(n)):
map(f, [$1..100]); # Robert Israel, Jan 10 2018

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

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

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

Sum_{k=1..n} a(k) ~ (2*zeta(3)/3) * n^3. - Amiram Eldar, Jan 12 2025

A297842 a(n) = Sum_{d|n} max(d, n/d)^3.

Original entry on oeis.org

1, 16, 54, 136, 250, 486, 686, 1152, 1485, 2250, 2662, 4016, 4394, 6174, 7000, 9280, 9826, 13554, 13718, 18250, 19208, 23958, 24334, 32560, 31375, 39546, 40824, 50078, 48778, 63182, 59582, 74752, 74536, 88434, 86436, 110106, 101306, 123462, 123032, 147024

Offset: 1

Seiichi Manyama, Jan 07 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Sum_{d|n} max(d, n/d)^k: A117003 (k=1), A297841 (k=2), this sequence (k=3), A297843 (k=4), A297844 (k=5).

Cf. A001158, A013662, A297793.

f[n_] := Block[{d = Divisors@ n}, Plus @@ (Max[#, n/#]^3 & /@ d)]; Array[f, 40] (* Robert G. Wilson v, Jan 07 2018 *)

PARI
```
{a(n) = sumdiv(n, d, max(d, n/d)^3)}
```

a(n) + A297793(n) = 2*A001158(n).

Sum_{k=1..n} a(k) ~ (zeta(4)/2) * n^4. - Amiram Eldar, Jan 12 2025

A297843 a(n) = Sum_{d|n} max(d, n/d)^4.

Original entry on oeis.org

1, 32, 162, 528, 1250, 2754, 4802, 8704, 13203, 21250, 29282, 44576, 57122, 81634, 102500, 139520, 167042, 225666, 260642, 341250, 393764, 497794, 559682, 715808, 781875, 971074, 1076004, 1310946, 1414562, 1743842, 1847042, 2236416, 2401124, 2839714, 3006052

Offset: 1

Seiichi Manyama, Jan 07 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Sum_{d|n} max(d, n/d)^k: A117003 (k=1), A297841 (k=2), A297842 (k=3), this sequence (k=4), A297844 (k=5).

Cf. A001159, A013663, A297794.

f[n_] := Block[{d = Divisors@ n}, Plus @@ (Max[#, n/#]^4 & /@ d)]; Array[f, 35] (* Robert G. Wilson v, Jan 07 2018 *)

PARI
```
{a(n) = sumdiv(n, d, max(d, n/d)^4)}
```

a(n) + A297794(n) = 2*A001159(n).

Sum_{k=1..n} a(k) ~ (2*zeta(5)/5) * n^5. - Amiram Eldar, Jan 12 2025

cp's OEIS Frontend

A297841 a(n) = Sum_{d|n} max(d, n/d)^2.

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A297842 a(n) = Sum_{d|n} max(d, n/d)^3.

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A297843 a(n) = Sum_{d|n} max(d, n/d)^4.

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