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

Author

Zak Seidov, Sep 27 2010

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..226
• Zak Seidov, Table of values of n, m
• Zak Seidov, A175849,A175850

Crossrefs

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

Programs

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 *)

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

Formula

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

Extensions

Data corrected and extended by Amiram Eldar, Feb 23 2020