A243008 Triangular numbers divisible by the square of the sum of their digits.

1, 10, 3240, 3321, 13041, 13203, 15400, 65341, 80200, 90100, 161028, 210276, 260281, 265356, 266085, 300700, 346528, 500500, 937765, 947376, 1043290, 1228528, 1313010, 1628110, 2049300, 2390391, 2421100, 3357936, 3746953, 4020030, 5250420, 6641190, 6857956, 6939675

Offset: 1

Author

K. D. Bajpai, Aug 20 2014

Keywords

• nonn
• base

Comments

Intersection of A000217 and A072081.

Examples

			a(3) = 3240 = 80 * (80 + 1)/2 is a triangular number. Since 3240 is divisible by (3 + 2 + 4 + 0)^2 = 81, it appears in the sequence.
a(3) = 3321 = 81 * (81 + 1)/2 is a triangular number. Since 3321 is divisible by (3 + 3 + 2 + 1)^2 = 81, it appears in the sequence.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..12445

Crossrefs

Cf. A000217, A072081, A076713, A118693.

Programs

Mathematica

Select[Table[n*(n + 1)/2, {n, 10000}], Divisible[#, Plus @@ IntegerDigits[#]^2] &]

PARI

for(n=1,10^4,s=n*(n+1)/2;if(s%(sumdigits(s)^2)==0,print1(s,", "))) \\ Derek Orr, Aug 23 2014