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

1,2

Links

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

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

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

Prog

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

Crossrefs

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

Sequence in context: A041141 A041142 A307947 * A294468 A041605 A239524

Adjacent sequences: A175846 A175847 A175848 * A175850 A175851 A175852

Keyword

nonn

Author

Zak Seidov, Sep 27 2010

Extensions

More terms from Amiram Eldar, Feb 23 2020

Status

approved