cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Jan 07 2018

Keywords

Links

Crossrefs

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.

Programs

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

Formula

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

Views

Author

Seiichi Manyama, Jan 07 2018

Keywords

Links

Crossrefs

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.

Programs

  • Mathematica
    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)}

Formula

a(n) + A297793(n) = 2*A001158(n).
Sum_{k=1..n} a(k) ~ (zeta(4)/2) * n^4. - Amiram Eldar, Jan 12 2025

A297844 a(n) = Sum_{d|n} max(d, n/d)^5.

Original entry on oeis.org

1, 64, 486, 2080, 6250, 16038, 33614, 67584, 118341, 206250, 322102, 515264, 742586, 1109262, 1525000, 2163712, 2839714, 3912786, 4952198, 6606250, 8201816, 10629366, 12872686, 16504000, 19534375, 24505338, 28815912, 35529998, 41022298, 50334302
Offset: 1

Views

Author

Seiichi Manyama, Jan 07 2018

Keywords

Comments

If p is a prime, then 2*p^5 belongs to this sequence. Conjecture: The converse is true. - Alexandra Hercilia Pereira Silva, Oct 04 2022

Links

Crossrefs

Sum_{d|n} max(d, n/d)^k: A117003 (k=1), A297841 (k=2), A297842 (k=3), A297843 (k=4), this sequence (k=5).
Cf. A001160, A013664, A297795.

Programs

  • Mathematica
    f[n_] := Block[{d = Divisors@ n}, Plus @@ (Max[#, n/#]^5 & /@ d)]; Array[f, 32] (* Robert G. Wilson v, Jan 07 2018 *)
  • PARI
    {a(n) = sumdiv(n, d, max(d, n/d)^5)}

Formula

a(n) + A297795(n) = 2*A001160(n).
Sum_{k=1..n} a(k) ~ (zeta(6)/3) * n^6. - Amiram Eldar, Jan 12 2025
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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