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

1,2

Links

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

Example

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

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 *)

Crossrefs

Includes A037156.

Sequence in context: A014007 A074254 A122963 * A219884 A042309 A215757

Adjacent sequences: A067517 A067518 A067519 * A067521 A067522 A067523

Keyword

base,easy,nonn

Author

Amarnath Murthy, Feb 14 2002

Extensions

More terms from Sascha Kurz, Mar 18 2002

Offset corrected by Sean A. Irvine, Dec 17 2023

Status

approved