%I #13 Oct 10 2021 06:11:28

%S 1,2,5,15,20,26,55,68,92,108,150,156,336,346,364,423,563,586,682,798,

%T 866,951,1194,1734,1888,2790,3102,3150,3506,4210,4611,5820,6766,6943,

%U 7665,7701,7888,8734,8772,9410,10114,10839,10969,11014,11453,11630,11947,12357

%N Integers m such that A006218(m) is triangular.

%H Chai Wah Wu, <a href="/A263457/b263457.txt">Table of n, a(n) for n = 1..1000</a>

%e If A027750 is displayed as a regular triangle:

%e 1; <--1

%e 1, 2; <--2

%e 1, 3; 1,

%e 2, 4; 1, 5; <--5

%e 1, 2, 3, 6; 1,

%e 7; 1, 2, 4, 8; 1,

%e 3, 9; 1, 2, 5, 10; 1,

%e 11; 1, 2, 3, 4, 6, 12; 1,

%e 13; 1, 2, 7, 14; 1, 3, 5, 15; <-- 15

%o (PARI) lista(nn) = {s = 0; for (n=1, nn, s += numdiv(n); if (ispolygonal(s, 3), print1(n, ", ")););}

%o (Python)

%o from sympy import integer_nthroot, divisor_count

%o A263457_list, s = [], 0

%o for n in range(1,10**4):

%o s += divisor_count(n)

%o if integer_nthroot(8*s+1,2)[1]:

%o A263457_list.append(n) # _Chai Wah Wu_, Oct 09 2021

%Y Cf. A000005, A006218, A027750, A175345.

%K nonn

%O 1,2

%A _Michel Marcus_, Oct 19 2015