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

1, 8, 9, 215, 458, 520, 2232, 3251, 3634, 5349, 9489, 10051, 10463, 14072, 14705, 17463, 27812, 46552, 55889, 79614, 100055, 106941, 110682, 113839, 119098, 181690, 197223, 214600, 270570, 287585, 333291, 384463, 439206, 443115, 608563, 767496, 1097448, 1335300

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, A175849,A175850

Crossrefs

Cf. A000203 (sigma(n) = sum of divisors of n), A000217 (triangular numbers), A175850 (corresponding values of m).

Programs

Mathematica

Select[Range[10^4], IntegerQ @ Sqrt[8*DivisorSigma[1, #*(#+1)/2] + 1] &] (* Amiram Eldar, Feb 23 2020 *)

PARI

{for(n=1, 10^7, m=sigma(n*(n+1)/2); issquare(d=1+8*m) && print1(n, ", "))} \\ edited by

Formula

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

Extensions

More terms from Amiram Eldar, Feb 23 2020