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

1,2

Comments

Intersection of A000326 and A005349.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000326, A005349, A076713.

Sequence in context: A009429 A207821 A297644 * A156236 A209481 A209340

Adjacent sequences: A242040 A242041 A242042 * A242044 A242045 A242046

Keyword

nonn,base

Author

K. D. Bajpai, Aug 12 2014

Status

approved