A175850 Numbers m with property that m-th triangular number is a sum of divisors of some k-th triangular number (A175849).

1, 13, 12, 384, 575, 783, 4095, 4607, 4095, 6912, 12543, 13824, 16895, 21504, 20735, 27264, 40959, 68256, 76544, 104832, 175104, 130559, 146432, 180224, 129024, 202239, 316224, 328320, 372735, 395199, 512000, 532575, 512000, 732159, 787968, 1181439, 1756160, 2253824

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..226

Zak Seidov, Table of values of n, m

Zak Seidov, A175849,A175850

Formula

sigma(T(k)) = T(m); A000203(A000217(k)) = A000217(m).

Example

Some pairs of k,m: 1,1; 8,13; 9,12; 215,384; 458,575; 520,783; 2232,4095; 3251,4607; 3634,4095; 5349,6912; 9489,12543; 10051,13824.

Mathematica

f[n_] := Sqrt[8*DivisorSigma[1, n*(n+1)/2] + 1]; (f /@ Select[Range[10^4], IntegerQ @ f[#] &] - 1)/2 (* Amiram Eldar, Feb 23 2020 *)

Prog

(PARI) {for(n=1, 10^7, m=sigma(n*(n+1)/2); issquare(d=1+8*m) && print1((sqrtint(d)-1)/2, ", "))} \\ edited by Michel Marcus, Feb 23 2020

Crossrefs

Cf. A000203 (sigma(n) = sum of divisors of n), A000217 (triangular numbers), A175849 (corresponding values of n).

Sequence in context: A113548 A249998 A195210 * A176306 A291368 A051392

Adjacent sequences: A175847 A175848 A175849 * A175851 A175852 A175853

Keyword

nonn

Author

Zak Seidov, Sep 27 2010

Extensions

Data corrected and extended by Amiram Eldar, Feb 23 2020

Status

approved