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.

A175927 Duplicate of A116990.

Original entry on oeis.org

1, 2, 11, 20, 40, 68, 92, 212, 236, 253, 266, 321, 328, 452, 582
Offset: 1

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Author

Zak Seidov, Oct 19 2010

Keywords

A256151 Triangular numbers n such that sigma(n) is a square number.

Original entry on oeis.org

1, 3, 66, 210, 820, 2346, 4278, 22578, 27966, 32131, 35511, 51681, 53956, 102378, 169653, 173755, 177906, 223446, 241860, 256686, 306153, 310866, 349866, 431056, 434778, 470935, 491536, 512578, 567645, 579426, 688551, 799480, 845650, 893116, 963966, 1031766, 1110795, 1200475, 1613706, 1719585
Offset: 1

Views

Author

Antonio Roldán, Mar 16 2015

Keywords

Comments

This sequence is the intersection of A000217 and A006532.
The corresponding triangular indices are in A116990. - Michel Marcus, Mar 17 2015

Examples

			3 is in the sequence because 3=2*3/2 is triangular, and sigma(3)=1+3=4=2^2 is square.
		

Crossrefs

Programs

  • Magma
    [n*(n+1) div 2: n in [1..2000] | IsSquare(SumOfDivisors(n*(n+1) div 2))]; // Vincenzo Librandi, Mar 17 2015
  • Mathematica
    Select[Accumulate[Range[0, 2000]], IntegerQ@Sqrt@DivisorSigma[1, #] &] (* Michael De Vlieger, Mar 17 2015 *)
  • PARI
    {for(i=1,2*10^3,n=i*(i+1)/2;if(issquare(sigma(n)),print1(n,", ")))}
    

A232355 Numbers k such that sigma(triangular(k)) = sigma(k)^2.

Original entry on oeis.org

1, 11, 695, 991, 2839, 3707, 9347, 10703, 12847, 27089, 42251, 56419, 74671, 115289, 168739, 191051, 219295, 233729, 280111, 300731, 326899, 353651, 430859, 611799, 642991, 661715, 1035827, 1116607, 1181579, 1234519, 1365491, 1485035, 1777099, 1854671, 1905875
Offset: 1

Views

Author

Alex Ratushnyak, Nov 22 2013

Keywords

Comments

Subsequence of A116990. - Michel Marcus, Jun 13 2015

Examples

			11 is in the sequence because sigma(11*12/2) = sigma(66) = 144 = 12^2 = sigma(11)^2.
		

Crossrefs

Cf. A000203 (sigma(n): sum of divisors of n), A000217 (triangular(n): = n*(n+1)/2).
Cf. A074285 (sigma(triangular(n))), A072861 (sigma(n)^2).
Cf. A116990 (indices of triangular numbers whose sum of divisors is square).

Programs

  • Magma
    [n: n in [1..7*10^5] | SumOfDivisors(n*(n+1) div 2) eq SumOfDivisors(n)^2]; // Vincenzo Librandi, Jun 13 2015
  • Mathematica
    Select[Range@1000000, DivisorSigma[1, #]^2==DivisorSigma[1, (# (# + 1)/2)] &] (* Vincenzo Librandi, Jun 13 2015 *)
  • PARI
    isok(n) = sigma(n)^2 == sigma(n*(n+1)/2); \\ Michel Marcus, Nov 23 2013
    

Extensions

More terms from Michel Marcus, Nov 23 2013
Showing 1-3 of 3 results.