A242043 Pentagonal numbers that are also Niven numbers.

1, 5, 12, 70, 117, 210, 247, 330, 715, 782, 1080, 1520, 1926, 2625, 2752, 3015, 3290, 3432, 4510, 5370, 5922, 6902, 7740, 8400, 9560, 11310, 12105, 13776, 14652, 15862, 17442, 21182, 21540, 23002, 24130, 26070, 27270, 30602, 31032, 32340, 34580, 38320, 39285

Offset: 1

Author

K. D. Bajpai, Aug 12 2014

Keywords

• nonn
• base

Comments

Intersection of A000326 and A005349.

Examples

			a(3) = 12 = 3*(3 * 3 - 1)/2 is a pentagonal number. Since 12 is divisible by 1 + 2 = 3, it is also a Harshad number and therefore in the sequence.
a(5) = 117 = 9*(3 * 9 - 1)/2 is a pentagonal number. Since 117 is divisible by 1 + 1 + 7 = 9 is also a Harshad number, and therefore in the sequence.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10344

Crossrefs

Cf. A000326, A005349, A076713.

Programs

Mathematica

A242043 = {}; Do[k = (3*n^2 - n)/2; If[IntegerQ[k/(Plus @@ IntegerDigits[k])], AppendTo[A242043, k]], {n, 300}]; A242043 (* Bajpai *)
Select[Table[n(3n - 1)/2, {n, 200}], Divisible[#, Plus@@IntegerDigits[#]] &] (* Alonso del Arte, Aug 16 2014 *)
Select[PolygonalNumber[5,Range[200]],Mod[#,Total[IntegerDigits[#]]]==0&] (* Harvey P. Dale, Nov 30 2022 *)