A067520 - OEIS

%I #24 Jan 18 2024 04:25:42

%S 1,10,21,45,55,120,171,300,465,666,820,1035,1485,1830,2016,2211,2628,

%T 2850,2926,3321,4095,5050,5565,5886,7260,8001,8911,10011,10440,13203,

%U 14196,16290,17955,18145,18528,19701,20910,22155,23436,24310,29646

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

%H Robert Israel, <a href="/A067520/b067520.txt">Table of n, a(n) for n = 1..10000</a>

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

%p f:= proc(n) local t;

%p    t:= n*(n+1)/2;

%p    if n mod convert(convert(t,base,10),`+`) = 0 then return t fi

%p end proc:

%p map(f, [$1..300]); # _Robert Israel_, Jan 18 2024

%t PolygonalNumber[Select[Range[300], Divisible[#, Total[IntegerDigits[# (# + 1) / 2]]]&]] (* _Paolo Xausa_, Jan 18 2024 *)

%Y Includes A037156.

%K base,easy,nonn

%O 1,2

%A _Amarnath Murthy_, Feb 14 2002

%E More terms from _Sascha Kurz_, Mar 18 2002

%E Offset corrected by _Sean A. Irvine_, Dec 17 2023