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.

A232554 Square numbers whose sum of square divisors is also square.

Original entry on oeis.org

1, 1764, 60516, 82369, 529984, 2056356, 2798929, 3534400, 18181696, 38900169, 96020401, 97121025, 335988900, 455907904, 457318225, 617820736, 1334513961, 1599200100, 2176689025, 3279852900, 4464244225, 8586616896, 15688815025, 24514164900, 33366502225
Offset: 1

Views

Author

Antonio Roldán, Nov 26 2013

Keywords

Examples

			60516 = 246^2. Sum of square divisors: 60516 + 15129 + 6724 + 1681 + 36 + 9 + 4 + 1 = 84100 = 290^2.

Links

Crossrefs

Cf. A035316, A046655, A232555, A232556, A232557.

Programs

  • Mathematica
    f[p_, e_] := (p^(2*(1 + Floor[e/2])) - 1)/(p^2 - 1); A035316[1] = 1; A035316[n_] := Times @@ f @@@ FactorInteger[n];
Select[Range[200000]^2, IntegerQ[Sqrt[A035316[#]]]&] (* Amiram Eldar, Aug 12 2023 *)
ssdQ[n_]:=IntegerQ[Sqrt[Total[Select[Divisors[n],IntegerQ[Sqrt[#]]&]]]]; Select[Range[200000]^2,ssdQ] (* Harvey P. Dale, Feb 03 2025 *)
  • PARI
    {for(n=1,10^5,m=n*n;k=sumdiv(m,d,d*issquare(d));if(issquare(k),print(m)))}

Formula

a(n) = A046655(n)^2.

A232555 Nonsquare numbers whose sum of proper square divisors is a square greater than 1.

Original entry on oeis.org

3528, 5292, 8820, 10584, 12348, 17640, 19404, 22932, 24696, 26460, 29988, 33516, 37044, 38808, 40572, 45864, 51156, 52920, 54684, 58212, 59976, 61740, 65268, 67032, 68796, 72324, 74088, 75852, 81144, 82908, 89964, 93492, 97020, 100548, 102312, 104076, 107604
Offset: 1

Views

Author

Antonio Roldán, Nov 26 2013

Keywords

Examples

			8820 is nonsquare number. Sum of proper square divisor: 1764 + 441 + 196 + 49 + 36 + 9 + 4 + 1 = 2500 = 50^2.

Links

Crossrefs

Subsequence of A232556.
Cf. A232554, A232557.

Programs

  • Mathematica
    f[p_, e_] := (p^(2*(1 + Floor[e/2])) - 1)/(p^2 - 1); A035316[1] = 1; A035316[n_] := Times @@ f @@@ FactorInteger[n]; sqQ[n_] := n>1 && IntegerQ[Sqrt[n]];
Select[Range[100000], !IntegerQ[Sqrt[#]] && sqQ[A035316[#]] &] (* Amiram Eldar, Aug 12 2023 *)
  • PARI
    {for(n=1,10^5,if(issquare(n)==0,k=sumdiv(n,d,d*issquare(d)); if(issquare(k)&&k>>1, print(n))))}

A232556 Numbers whose sum of proper square divisors is a square greater than 1.

Original entry on oeis.org

900, 3528, 4900, 5292, 8820, 10404, 10584, 12348, 17640, 19404, 22932, 24696, 26460, 29988, 33516, 37044, 38808, 40572, 45864, 51156, 52920, 54684, 58212, 59976, 61740, 65268, 67032, 68796, 72324, 74088, 75852, 79524, 81144, 81796, 82908, 89964, 93492
Offset: 1

Views

Author

Antonio Roldán, Nov 26 2013

Keywords

Examples

			Sum of proper square divisors of 5292: 1764 + 441 + 196 + 49 + 36 + 9 + 4 + 1 = 2500 = 50^2 is square number.

Links

Crossrefs

Disjoint union of A232555 and A232557.
Cf. A232554.

Programs

  • Mathematica
    f[p_, e_] := (p^(2*(1 + Floor[e/2])) - 1)/(p^2 - 1); A035316[1] = 1; A035316[n_] := Times @@ f @@@ FactorInteger[n]; sqQ[n_] := n>1 && IntegerQ[Sqrt[n]];
Select[Range[100000], sqQ[A035316[#] - If[IntegerQ[Sqrt[#]], #, 0]] &] (* Amiram Eldar, Aug 12 2023 *)
  • PARI
    {for(n=1,10^5,k=sumdiv(n,d,d*issquare(d)*(d>1,print(n)))}
Showing 1-3 of 3 results.

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

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