A175849 - OEIS

%I #12 Feb 23 2020 07:09:17

%S 1,8,9,215,458,520,2232,3251,3634,5349,9489,10051,10463,14072,14705,

%T 17463,27812,46552,55889,79614,100055,106941,110682,113839,119098,

%U 181690,197223,214600,270570,287585,333291,384463,439206,443115,608563,767496,1097448,1335300

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

%H Amiram Eldar, <a href="/A175849/b175849.txt">Table of n, a(n) for n = 1..226</a>

%H Zak Seidov, <a href="http://zak08.livejournal.com/24800.html">A175849,A175850</a>

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

%e 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.

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

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

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

%K nonn

%O 1,2

%A _Zak Seidov_, Sep 27 2010

%E More terms from _Amiram Eldar_, Feb 23 2020