

A242043


Pentagonal numbers that are also Niven numbers.


1



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
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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 is 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 *)


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



