A175850 - OEIS

%I #18 Feb 23 2020 07:09:33

%S 1,13,12,384,575,783,4095,4607,4095,6912,12543,13824,16895,21504,

%T 20735,27264,40959,68256,76544,104832,175104,130559,146432,180224,

%U 129024,202239,316224,328320,372735,395199,512000,532575,512000,732159,787968,1181439,1756160,2253824

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

%H Amiram Eldar, <a href="/A175850/b175850.txt">Table of n, a(n) for n = 1..226</a>

%H Zak Seidov, <a href="/A175850/a175850.txt">Table of values of n, m</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 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 *)

%o (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

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

%K nonn

%O 1,2

%A _Zak Seidov_, Sep 27 2010

%E Data corrected and extended by _Amiram Eldar_, Feb 23 2020