A067520 Triangular numbers whose index is a multiple of the sum of their digits.

1, 10, 21, 45, 55, 120, 171, 300, 465, 666, 820, 1035, 1485, 1830, 2016, 2211, 2628, 2850, 2926, 3321, 4095, 5050, 5565, 5886, 7260, 8001, 8911, 10011, 10440, 13203, 14196, 16290, 17955, 18145, 18528, 19701, 20910, 22155, 23436, 24310, 29646

Offset: 1

Author

Amarnath Murthy, Feb 14 2002

Keywords

• base
• easy
• nonn

Examples

			T(30) = 465 and 30 = 2*(4+6+5).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Includes A037156.

Programs

Maple

f:= proc(n) local t;
   t:= n*(n+1)/2;
   if n mod convert(convert(t,base,10),`+`) = 0 then return t fi
end proc:
map(f, [$1..300]); # Robert Israel, Jan 18 2024

Mathematica

PolygonalNumber[Select[Range[300], Divisible[#, Total[IntegerDigits[# (# + 1) / 2]]]&]] (* Paolo Xausa, Jan 18 2024 *)

Extensions

More terms from Sascha Kurz, Mar 18 2002

Offset corrected by Sean A. Irvine, Dec 17 2023